Influence of cationic substitution on hyperfine...

Charles University in PragueFaculty of Mathematics and Physics

DIPLOMA THESIS

Richard Reznıcek

Influence of cationic substitution on hyperfineinteractions in magnetite

Department of Low Temperature Physics

Supervisor: prof. RNDr. Helena Stepankova, CSc.

Study program: Physics of Condensed Matter and Materials

2010

I would like to express my gratitude to my supervisor prof. RNDr. HelenaStepankova, CSc. for her guidance and for provided advice. I am also obligedto my consultant Mgr. Vojtech Chlan. I wish to thank those who kindly providedthe samples: prof. V. A. M. Brabers from Technical University of Eindhoven,prof. J. M. Honig from Purdue University in West Lafayette, prof. dr hab. Ing.Andrzej Koz lowski and prof. dr hab. Ing. Zbigniew Kakol from AGH Universityof Krakow. I am grateful to Ing. Pavel Novak, DSc. for his hints. Finally, I wishto thank my sister Alena for language corrections.

Prohlasuji, ze jsem svou diplomovou praci napsal samostatne a vyhradne s pouzitımcitovanych pramenu. Souhlasım se zapujcovanım prace.

I hereby confirm that the diploma thesis submitted is entirely my own work andall other sources used are cited appropriately. I agree with lending of the thesis.

Prague, 12th April 2010 Richard Reznıcek

2

Contents

1 Introduction 6

2 NMR Method 72.1 NMR Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Nuclear Magnetic Moment . . . . . . . . . . . . . . . . . . . 72.1.2 Interaction with Magnetic Field . . . . . . . . . . . . . . . . 72.1.3 Effect of RF Field . . . . . . . . . . . . . . . . . . . . . . . . 82.1.4 Nuclear Magnetization . . . . . . . . . . . . . . . . . . . . . 82.1.5 Bloch equations . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Pulse Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.1 Free Induction Decay . . . . . . . . . . . . . . . . . . . . . . 102.2.2 Spin Echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.3 CPMG Sequence . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 NMR Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 NMR Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 NMR in Magnetics . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Structure of Magnetite 153.1 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Magnetic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 NMR in Magnetite . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Substitution and Defects in Magnetite . . . . . . . . . . . . . . . . 19

4 Experiments and Discussion 234.1 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Experimental Settings and the Data Processing . . . . . . . . . . . 244.3 Results on Zinc Substituted Magnetite Samples . . . . . . . . . . . 27

4.3.1 Spectra below the Verwey Transition Temperature . . . . . . 274.3.2 Spectra above the Verwey Transition Temperature . . . . . . 294.3.3 Temperature Dependences of Spectra above the Verwey Tran-

sition Temperature . . . . . . . . . . . . . . . . . . . . . . . 334.3.4 Temperature Dependences of Spectral Signal Frequencies . . 404.3.5 Temperature Dependences of HWHM of the A Lines . . . . 43

4.4 Results on Titanium Substituted Magnetite Samples . . . . . . . . 434.4.1 Spectra below the Verwey Transition Temperature . . . . . . 434.4.2 Spectra above the Verwey Transition Temperature . . . . . . 454.4.3 Temperature Dependences of Spectra above the Verwey Tran-

sition Temperature . . . . . . . . . . . . . . . . . . . . . . . 48

3

4.4.4 Temperature Dependences of Spectral Signal Frequencies . . 554.4.5 Temperature Dependences of HWHM of the A Lines . . . . 57

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5 Conclusion 71

A Temperature Dependences of NMR Spectra of Zinc SubstitutedMagnetite Samples 73

B Temperature Dependences of Spectral Signal Frequencies of ZincSubstituted Magnetite Samples - Tables 83

C Temperature Dependences of HWHM of the A Lines of Zinc Sub-stituted Magnetite Samples - Tables 90

D Temperature Dependences of NMR Spectra of Titanium Substi-tuted Magnetite Samples 92

E Temperature Dependences of Spectral Signal Frequencies of Ti-tanium Substituted Magnetite Samples - Tables 102

F Temperature Dependences of HWHM of the A Lines of TitaniumSubstituted Magnetite Samples - Tables 109

Bibliography 111

4

Nazev prace: Vliv substituce kationtu na hyperjemne interakce v magnetituAutor: Richard ReznıcekKatedra (ustav): Katedra fyziky nızkych teplotVedoucı diplomove prace: prof. RNDr. Helena Stepankova, CSc.e-mail vedoucıho: [email protected]

Abstrakt: Tematem predlozene prace je studium souboru monokrystalickych vzor-ku magnetitu se substitucemi zinku a titanu metodami NMR. Ionty substitucezinku Zn2+ nahrazujı cast zelezitych iontu v tetraedrickych (A) pozicıch, zatımcoionty titanu Ti4+ obsazujı oktaedricke (B) pozice nahrazujıce ionty zeleza Fe2.5+.Hyperjemne interakce a lokalnı elektronova struktura jsou citlive na prıtomnostsubstituce. Obzvlaste zajımavy je prıpad, kdyz valence iontu substituce je odlisnaod valence nahrazovaneho iontu. Resonancnı frekvence jader v okolı substitucejsou posunuty v dusledku zmeneneho hyperjemneho pole, je tedy mozne pozoro-vat satelitnı cary ve spektrech NMR. Teplotnı zavislosti spekter nad Verweyovymprechodem byly mereny v nulovem vnejsım magnetickem poli a byla take zmerenaspektra NMR pri teplote 4,2 K. Sestavene teplotnı zavislosti frekvencı hlavnıchcar a satelitnıch signalu ve spektrech nad Verweyovym prechodem byly porovnanys daty pro cisty magnetit a magnetit s dalsımi substitucemi a kationtovymi vakan-cemi. Dale byly nad Verweyovym prechodem nalezeny a diskutovany zmeny sırekA car s teplotou.

Klıcova slova: NMR, magnetit, substituce Zn, substituce Ti, elektronova struktura

Title: Influence of cationic substitution on hyperfine interactions in magnetiteAuthor: Richard ReznıcekDepartment: Department of Low Temperature PhysicsSupervisor: prof. RNDr. Helena Stepankova, CSc.Supervisor’s e-mail address: [email protected]

Abstract: The subject matter of the present work is a study of a series of singlecrystal samples of magnetite with substitutions of zinc and titanium by means ofthe NMR method. Ions of the zinc substitution Zn2+ replace a part of ferric ionsat tetrahedral (A) sites, while the titanium ions Ti4+ occupy octahedral (B) sitesreplacing iron ions Fe2.5+. Hyperfine interactions and local electronic structureare sensitive to the presence of substitution. The case when the valence of thesubstitution ion is different from that of the replaced ion is of a particular inte-rest. Resonance frequencies of nuclei in the neighbourhood of the substitution areshifted due to the modified hyperfine field, thus satellite lines can be observed inNMR spectra. Temperature dependences of spectra above the Verwey transitionwere measured in a zero external magnetic field. Additionally, NMR spectra werealso acquired at the temperature of 4.2 K. Temperature dependences of frequen-cies of main lines and satellite signals in the spectra above the Verwey transitionwere constructed and compared to the data for pure magnetite and magnetitewith other substitutions and with cationic vacancies. Furthermore, variations ofwidths of A lines against the temperature above the Verwey transition were foundand discussed.

Keywords: NMR, magnetite, Zn substitution, Ti substitution, electronic structure

5

mailto:[email protected]

mailto:[email protected]

Chapter 1

Introduction

Magnetite (Fe3O4), one of the first discovered magnetic materials, exhibits manyinteresting physical properties. The most characteristic feature of this compoundis a structural phase transition of the first order at ≈ 120 K, which is known asthe Verwey transition. During this transition, changes of other physical proper-ties of this substance occur, e.g. specific heat anomaly and an abrupt change ofelectrical conductivity. Despite the longstanding research of magnetite, its elec-tronic structure and the principle of the Verwey transition are still not completelyresolved. A broad range of applications of magnetite-derived ferrites, especially inelectrotechnics and electronics, and a recent utilization of these materials in otherfields, e.g. in biomedical applications, represent another cogent argument for bothfundamental and applied physical research of magnetite.

Physical properties, especially the electronic structure and the Verwey transi-tion, are influenced by the presence of substitution or vacancies in a sample. Thusa systematical study of substituted and non-stoichiometric magnetite can bringnew information important for our understanding of the physical properties andprocesses related to this compound. Nuclear magnetic resonance is particularlysuitable for microstructure investigation of magnetite as the resonating 57Fe nu-clei serve as a local hyperfine field probe. Moreover, the NMR method providesthe highest resolution of all hyperfine methods, which makes it possible to ob-serve even fine structures in spectra. The contribution of NMR in the magnetiteresearch can be documented for example by articles [1] and [2], which proposethe charge density wave model of charge ordering in magnetite below the Verweytransition based on NMR experiments.

Existing works employing NMR on substituted magnetite focused mainly onsubstitution of aluminium ions Al3+ [3], [4] and gallium ions Ga3+ [5]. NMR spec-trum of magnetite substituted by titanium ions Ti4+ at 273 K was published onlyin [6], spectra and relaxation times of zinc substituted magnetite at 4.2 K, 198 Kand 273 K were measured in [7]. This work aims to measure temperature depen-dence of NMR spectra above the Verwey transition of titanium and zinc substi-tuted magnetite samples. Results of performed experiments are analyzed and com-pared to data for magnetite with other substitutions and for non-stoichiometricmagnetite in order to obtain information about the impact of substitutions on theNMR spectra and on the magnetic and electronic structure of magnetite.

6

Chapter 2

NMR Method

2.1 NMR Principles

2.1.1 Nuclear Magnetic Moment

Vector sum of spin and orbital angular momenta of nucleons is called nuclear

spin→I . Absolute value of nuclear spin |

→I | is connected to nuclear spin quantum

number I (0, 1/2, 1, 3/2, ...) by relation

|→I | = ~

√I (I + 1). (2.1)

The z-component is given by nuclear spin magnetic quantum number m (−I,−I + 1, ..., I − 1, I)

Iz = ~m. (2.2)

Nuclear magnetic moment is related to nuclear spin and gyromagnetic ratio γ

→µ = γ

→I , (2.3)

for z-component appliesµz = γIz. (2.4)

2.1.2 Interaction with Magnetic Field

Interaction of the nuclear magnetic moment→µ with an external (static) magnetic

field→B0 is described by Hamiltonian

H0 = −→µ ·

→B0. (2.5)

Let→B0 = (0, 0, B0) and rewrite the Hamiltonian as

H0 = −γIzB0. (2.6)

Energy eigenvalues are then determined by the values of magnetic quantum num-ber m (see (2.2)):

Em = −γ~mB0. (2.7)

The set of 2I + 1 energy eigenvalues forms Zeeman multiplet of equidistant en-ergy levels corresponding to particular space orientations of the nuclear magneticmoment.

7

2.1.3 Effect of RF Field

If we consider the presence of an external radio-frequency (RF) magnetic field→B1 = (B1 cos ωzt, B1 sin ωzt, 0) (ωz is angular frequency) in addition to the static

magnetic field→B0 = (0, 0, B0), we can write the Hamiltonian of the interaction of

the nuclear magnetic moment with the magnetic field in the form

H = H0 + H1 (t) , (2.8)

where

H1 = −→µ ·

→B1 = −γB1

(Ix cos ωzt + Iy sin ωzt

)= −γB1

2

(I−eiωzt + I+e−iωzt

)(2.9)

(I− and I+ are lowering and raising operators).The RF field can induce transitions between the levels of Zeeman multiplet.

This effect is called the nuclear magnetic resonance (NMR). The probability oftransition between states with quantum numbers m and m’ is in approximationof perturbation theory (valid for B1 << B0) proportional to perturbation matrixelement

Pm’,m ∼ |〈m’|H1|m〉|2. (2.10)

Considering the form of Hamiltonian (2.9) and the properties of ladder operators,we notice that only transitions between neighbouring levels are allowed, i.e. m’ =m± 1.

The transition between neighbouring levels of Zeeman multiplet is accompaniedby emission or absorption of energy quantum |∆E| = γ~B0 (see (2.7)). This energyquantum can be written as ∆E = ~ω0 and thus we obtain the resonance condition[8]

ω0 = γB0, (2.11)

where ω0 is called Larmor frequency.

2.1.4 Nuclear Magnetization

Macroscopic nuclear magnetization→M can be understood as a sum of magnetic

moments→µi of nuclei in volume V

→M=

N∑i=1

→µi

V, (2.12)

where N is the number of nuclei in the specified volume.Assuming the thermal equilibrium with lattice at temperature T , the occupa-

tion probability pm for level Em of Zeeman multiplet corresponding to magneticquantum number m is determined by Boltzmann distribution

pm =e− Em

kBT∑Im’=−I e

− Em’kBT

, (2.13)

8

where kB is the Boltzmann constant. The equilibrium nuclear magnetization→M0 =

(0, 0, M0) in external magnetic field→B0 = (0, 0, B0) can be obtained by employing

relations (2.4) and (2.2):

M0 =N∑

i=1

γ~V

I∑m=−I

mpm =Nγ~V

∑Im=−I me

− EmkBT∑I

m=−I e− Em

kBT

=Nγ~V

IBI

(Iγ~B0

kBT

), (2.14)

where BI (x) stands for Brillouin function. For Iγ~B0

kBT<< 1 we get the equation

M0 =Nγ2~2

V

I (I + 1) B0

3kBT(2.15)

corresponding to Curie’s law.

2.1.5 Bloch equations

Now we consider a condensed matter placed in an external magnetic field→B=

→B0 +

→B1 (t), where B1 << B0,

→B0 = (0, 0, B0),

→B1 = (B1 cos ωzt, B1 sin ωzt, 0) and

→ωz is the frequency of the RF field. The motion of nuclear magnetization

→M is

phenomenologically described by Bloch equations:

dMx

dt= γ

( →M ×

→B

)x− Mx

T2

(2.16)

dMy

dt= γ

( →M ×

→B

)y− My

T2

(2.17)

dMz

dt= γ

( →M ×

→B

)z− Mz −M0

T1

(2.18)

where T1 is called spin-lattice (longitudinal) relaxation time, T2 is spin-spin (trans-

verse) relaxation time and→M0 = (0, 0, M0) is equilibrium magnetization in the field

→B0.

The first term at the right side of Bloch equations describes how thenuclear magnetization is influenced by torsional moment of the external field. Inthe absence of an RF field (i.e. B1 = 0), nuclear magnetization exercises Larmor

precession around the direction of the static field→B0 at Larmor frequency

→ω0 = −γ

→B0. (2.19)

When the RF field is present, we should take advantage of the transformation ofequations (2.16), (2.17) and (2.18) into the system of coordinates rotating with

the RF field, which replaces the time-dependent field→B in the expressions by a

time-independent effective field

→Bef =

(B1, 0, B0 +

ωz

γ

). (2.20)

In the rotating system of coordinates, nuclear magnetization precedes around the

effective field→Bef at a frequency

→ω1 = −γ

→Bef .

9

Now we consider the RF field in the form of a single pulse of length τ . We

start at B1 = 0 and→M ||

→B0, then we apply the RF pulse and at the end of the

pulse the nuclear magnetization is tilted at an angle (referenced to z-axis)

θ = γB1τ. (2.21)

This principle can be used to adjust the precession angle.The second term at the right side of Bloch equations describes how

the nuclear magnetization returns to equilibrium. The last term at the right sideof equation (2.18) corresponds to the interaction of nuclear spins and lattice. Therate of energy transfer from spin system to lattice after tilting nuclear magneti-zation from equilibrium is characterized by spin-lattice relaxation time T1. Thesecond terms at the right side of equations (2.16) and (2.17) describe the decayof transverse components of nuclear magnetization caused by fluctuations of Lar-mor precession frequencies of particular nuclear magnetic moments. In the ideal

case of an absolutely homogenous field→B0, the decay is characterized by spin-spin

relaxation time T2. In reality, however, Larmor frequencies of individual nuclear

magnetic moments differ due to local inhomogeneities of the field→B0, which re-

sults in faster decay characterized by time T ?2 because of out-of-phase motion of

individual moments.

2.2 Pulse Sequences

Today’s NMR experiments are almost exclusively based on pulse methods, i.e.

RF field→B1 (t) is applied in the form of short pulses and the response of nuclear

magnetization is detected in the time after or between pulses. The length of pulsesis assumed to be far shorter than spin-lattice and spin-spin relaxation times. Thischapter contains short characteristics of two basic pulse sequences (FID and spinecho) and CPMG sequence, which was employed in performed experiments.

2.2.1 Free Induction Decay

Pulse sequence for free induction decay measurements consists of a single RF pulseat Larmor frequency of length corresponding to π/2 tilt of nuclear magnetizationaccording to (2.21). Such pulse is called π/2-pulse. Transverse component ofnuclear magnetization can be detected after the end of the pulse as a free induction

decay signal. In case of an absolutely homogenous field→B0, the amplitude A of

the signal would decay in time t (t = 0 set at the start of pulse) as

A (t) ∼ exp

(− t

T2

). (2.22)

However, local inhomogeneities of the magnetic field→B0 cause much faster decay

A (t) ∼ exp

(− t

T ?2

). (2.23)

10

2 twtw0

π/2 π FIDspin echo

Figure 2.1: Free induction decay and spin echo sequences

2.2.2 Spin Echo

The sequence for spin echo signal measurement can be obtained by appending thesecond RF pulse at Larmor frequency of length corresponding to π tilt of nuclearmagnetization (see (2.21)) to the FID sequence. Time interval tw between theπ/2-pulse and this π-pulse should be shorter than spin-spin relaxation time T2.The application of π-pulse flips the transverse component of nuclear magnetization

through π angle around the→B1 direction. Thus the local magnetization vectors

get aligned in the time 2tw and the transverse component of nuclear magnetizationcan be observed as a spin echo signal. Amplitude of spin echo signal follows therelation (2.22).

2.2.3 CPMG Sequence

Spin echo sequence can be further extended by appending additional π-pulseswhile keeping 2tw time spacing between adjacent π-pulses. In this case, the spinecho signal can be detected in each time window between π-pulses (and of coursealso after the last π-pulse), while the amplitudes of these echoes correspond torelation (2.22). This pulse sequence, which is named Carr-Purcell sequence, isvery sensitive to improperly adjusted π-pulse length and intensity, because anydeviation causes nuclear magnetization to point slightly out of the transverse planeand these errors cumulate through the sequence. The abovementioned problemis solved in Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence by introducingπ/2 phase shift of π/2-pulse relative to π-pulses’ phase. As was shown in [9], thedescribed errors are not cumulative in CPMG sequence.

11

18tw16tw14tw12tw10tw8tw6tw4tw2twtw0

π/2 π π π π π π π π π

FIDspin echoes

Figure 2.2: CPMG pulse sequence

2.3 NMR Spectrum

NMR spectrum is a distribution of resonance (Larmor) frequencies of nuclearmagnetic moments in an investigated sample excited by the pulse sequence. Inorder to obtain the spectrum, Fourier transform has to be applied to signal in thetime domain acquired during pulse method experiments. Free induction decay orspin echo signal can be usually transformed directly, whereas in case of the signalfrom the CPMG experiment, it is useful to average corresponding data pointsfrom detected echoes in order to obtain waveform similar to the signal of one spinecho while taking advantage of significantly better signal-to-noise ratio (SNR).However, the shape of the spectrum can be influenced by frequency dependenceof spin-spin relaxation time T2 if averaged echoes originate from time interval oflength comparable to T2.

2.4 NMR Spectrometer

Pulse NMR spectrometer, a simplified block diagram of which is in figure 2.3, isused to apply the desired sequence of RF pulses to a sample and to record thenuclear magnetization response.

A pulse generator is responsible both for the proper length and timing ofexcitation pulses and for triggering of signal acquisition. An RF signal at desiredfrequency and with appropriate phase is generated by a frequency synthesizer.A modulator transforms this signal into RF pulses, which are then appropriatelyattenuated and led into a (fixed gain) power amplifier in order to achieve requestedpulse intensity. During excitation period, the power amplifier output is connectedto the probe consisting of an LC resonance circuit (sample is placed in the coil)through the RX/TX switch, while the preamplifier input is isolated. Throughoutthe detection period, the power amplifier output is isolated from the probe anda signal induced in the LC circuit by the motion of transverse component ofnuclear magnetization is connected to the preamplifier input. Amplified NMRsignal is mixed with the second RF signal provided by the frequency synthesizerat frequency higher (or lower) by intermediate frequency (IF) than the excitationfrequency. The resulting signal is further amplified in an IF amplifier and thensent into an I/Q detector. In-phase and quadrature signals from the outputs of the

12

detector are digitized by an A/D converter and stored in a memory. An importantfeature of this data acquisition is the ability to perform coherent summation of thesignal, i.e. the pulse sequence is repeated many times and the corresponding datapoints from all scans are summed in order to improve the signal-to-noise ratio(SNR is proportional to a square root of number of scans). Acquired data aretransferred into a computer for subsequent processing. This computer serves alsofor control of the spectrometer by operator. The purpose of a stable frequencyreference is to ensure that all RF signals are coherent and that clock signals forrelevant logic circuits are synchronous.

Figure 2.3: Simplified block diagram of pulse NMR spectrometer

2.5 NMR in Magnetics

A major part of a local magnetic field at nuclei in magnetically ordered matter isrepresented by hyperfine field originating from electron magnetic moments:

→Bh = −µ0µB

2π

∑i

→l i

r3i

+

→s i

r3i

−3

(→s i ·

→r i

)→r i

r5i

+8π

3

→s iδ

(→r i

) , (2.24)

where→r i are positions (relative to nucleus),

→l i stand for orbital moments and

→s i are spins of particular electrons, µ0 denotes permeability of vacuum and µB isBohr magneton. The first term in this equation is the magnetic field coming fromelectron orbital moments, other terms describe field corresponding to interactionbetween nucleus and electron spins, where the last term belongs to Fermi contactinteraction. Time mean value of hyperfine field in magnetic substances is high evenin a zero external magnetic field, which allows us to perform NMR experimentsin these materials without the need for an external static magnetic field.

Hyperfine field is strongly dependent on crystal, electronic and magnetic struc-ture of the sample in the vicinity of a nucleus. As a result, splitting of energy

13

levels of nuclei in crystallographically or magnetically nonequivalent positions isdifferent. Also the presence of a defect near a nucleus influences the energy levelsplitting. Differences in splitting of both origins can be observed in a measuredNMR spectrum. However, significant differences of hyperfine field strength indistinct crystallographic positions imply a wide spectral range.

The interaction of an external RF field with nuclear magnetic moments wasdescribed in previous paragraphs, but we also have to mention the interaction ofthis field with electron magnetic moments, which produces the oscillating compo-nent of a hyperfine field. Thus total RF field interacting with nuclear momentsin magnetics is much stronger than an external RF field. Ratio of the total RFfield amplitude B2 and the external RF field amplitude B1 is called enhancement(amplification) factor

η =B2

B1

. (2.25)

Values of η depend on the material and typically fall in the range from 1 to 104.This factor is usually different for nuclei in magnetic domains, where enhancementis caused by rotation of electron magnetization, than for those in walls, whereenhancement process is based on wall motion.

The coupling between nuclear and electron systems is also responsible for theamplification of the detected signal.

14

Chapter 3

Structure of Magnetite

3.1 Crystal Structure

Chemical formula for magnetite is Fe3O4. The most typical feature of this com-pound is the Verwey phase transition at TV ≈ 120 K. This transition is accompa-nied by a change of crystal structure, specific heat anomaly and an abrupt changeof electrical conductivity by two orders of magnitude. Detailed review can befound in [10] and [11].

At a temperature above the Verwey transition, magnetite has a cubic inversespinel structure belonging to a space group Fd3m−O7

h. Elementary cell (lat-tice parameter a = 8.398 A [12]) contains 32 oxygen ions O2− arranged in a facecentered cubic lattice. There are 64 tetrahedral and 32 octahedral interstitial posi-tions between the oxygen ions in this lattice. Ferric ions Fe3+ occupy 8 tetrahedral(A) sites, while iron ions with mixed valency Fe2.5+ are located at 16 octahedral(B) sites. Elementary cubic cell can be divided into 8 octants of two types withdifferent iron ion positions as shown in figure 3.1. (See [13], [14] for details.) Thesymmetry of occupied crystallographic positions can be found in table 3.1 [15].

The structure of magnetite below the Verwey transition is monoclinic of space

group Cc. Axes of elementary monoclinic cell→am,

→b m a

→c m correspond to di-

rections[110

], [110] a [001] in cubic lattice above the Verwey transition and the

dimensions of the monoclinic cell expressed using the cubic cell parameter are√2a ×

√2a × 2a. Lattice parameters at temperature 10 K are am = 11.868 A,

bm = 11.851 A and cm = 16.752 A [16]. Angle between the monoclinic and→am

axes is β = 90.2365 (2)◦ [17].

15

Figure 3.1: Magnetite elementary cell above the Verwey transition

Table 3.1: Occupied crystallographic sites in cubic magnetite structure (originat tetrahedral site) [15]

Occupied

positionsMultiplicity

Wyckoff

symbolSymmetry Coordinates

O2- ion sites 32 e 3m

μ, μ, μ ;

μ, μ, μ ;

μ, μ, μ;

μ, μ, μ;

1/4 -μ, 1/4 - μ, 1/4 - μ;

1/4 - μ, 1/4 + μ, 1/4+ μ;

1/4 + μ, 1/4 - μ, 1/4+μ;

1/4 + μ, 1/4+ μ, 1/4 - μ; Fe2.5+ ion

B sites16 d 3m 5/8,5/8,5/8; 5/8,7/8,7/8; 7/8,5/8,7/8; 7/8,7/8,5/8;

Fe3+ ion

A sites8 a 43m 0,0,0; 1/4,1/4,1/4;

16

3.2 Magnetic Structure

Magnetite is a ferrimagnetic material with paramagnetic transition at a temper-ature TC ≈ 860 K. Magnetic moments of iron ions in A sites are anti-parallel tothose of iron ions in B sites [14]. Total magnetic moment has a direction of mo-ments of iron ions in B positions. The principal interactions responsible for mag-netic ordering in magnetite are double exchange and superexchange interactions.Both the experimental data [18] for temperature dependence of magnetizations ofA and B sublattices and the curves calculated [19] using Kubo-Ohata mean fieldtheory [20] are shown in figure 3.2.

Figure 3.2: Comparison of the calculated and experimental reduced magnetiza-tions in magnetite [19]

An easy magnetization direction in monoclinic lattice of magnetite below theVerwey transition is [001]. The number of magnetically nonequivalent positionsthen equals the number of crystallographically non-equivalent positions, i.e. thereare 8 magnetically non-equivalent A positions and 16 magnetically non-equivalentB positions.

In the temperature range between the Verwey transition and the spin reori-entation transition (≈ 125− 130 K), the easy magnetization direction in cubiclattice is [001]. In this case all A positions are magnetically equivalent and alsoall B positions are magnetically equivalent.

Easy magnetization direction above spin reorientation transition is [111]. Inthis situation all A positions are magnetically equivalent, while B positions aredivided into two groups of magnetically equivalent positions B1 a B2 in ratio 1:3.

17

3.3 NMR in Magnetite

NMR is a very suitable method for a study of crystal, electronic and magneticstructure of magnetite as the resonating nuclei 57Fe represent a local hyperfinemagnetic field probe. Each group of magnetically equivalent crystallographic po-sitions of iron ions gives rise to one spectral line, the intensity of which is pro-portional to the count of resonating nuclei in this group. Considering the afore-mentioned phase transitions in magnetite, different structure of spectra can beexpected for temperatures below the Verwey transition, between the Verwey andthe spin reorientation transitions and above the spin reorientation transition, ascan be seen in figure 3.3 [21]. The structure of spectra in figure 3.3 corresponds tothe crystal and magnetic structure of magnetite at particular temperature. Thereare 8 A lines (two of them are overlapping) and 16 B lines (one of them is over-lapped by A lines) resolved in the spectrum below the Verwey transition. One Aline and one B line can be found in the spectrum measured at temperature in be-tween the Verwey and the spin reorientation transitions. The spectrum acquiredabove the temperature of the spin reorientation transition contains one A line andtwo B lines (B1 and B2) with an intensity ratio 1:3.

Figure 3.3: NMR spectra of pure magnetite measured at temperature below theVerwey transitions (a), between the Verwey and the spin reorientation transition(b) and above spin reorientation transition (c) [21]

Individual lines in NMR spectra of magnetite were identified in papers [2] and[1]. Temperature dependence of frequencies of individual lines in the range from4,2 K to 135 K can be also found in [2], while the dependences above the Verweytransition up to 400 K for A line and up to 320 K for both A and B lines werepublished in [3] for pure and Al-substituted samples and in [22] for pure magnetiteand magnetite with vacancies, respectively. Angular variations of frequencies of

18

spectral lines in an external magnetic field were reported in [1].Spin-lattice relaxation times of particular spectral lines measured at temper-

ature 4,2 K in [2] are comparable, whereas spin-spin relaxation times differ byorders of magnitude. Temperature dependences of both spin-lattice and spin-spinrelaxation times below the Verwey transition were published in [23]. Dependencesof relaxation times of all A lines are of similar character, the same applies for theB lines.

3.4 Substitution and Defects in Magnetite

Physical properties of magnetite can be strongly influenced by the presence ofstructural defects and substitutions at cation sites. In particular, the temperatureof the Verwey transition decreases with increasing concentration of substitutionor vacancies in a sample – see figure 3.4 [24]. Moreover, when the concentrationreaches a limit marked in figure 3.4 by vertical line, a change of the Verwey tran-sition from the transition of the first order to the transition of a higher order wasreported [24], [25].

Figure 3.4: Variation of the Verwey transition temperature against sample com-position. The region on the left from a vertical line corresponds to the first ordertransition. [24]

Existing NMR studies of samples with substitutions or structural defects con-cern mainly substitution of aluminium ions Al3+ [3], [4] and gallium ions Ga3+ [5]and vacancies in non-stoichiometric magnetite [22]. NMR spectra and relaxationtimes of magnetite with substitution of zinc Zn2+ ions measured at 4.2 K, 198 Kand 273 K were published in [7]. Spectrum of magnetite substituted by titaniumions Ti4+ at 273 K was reported in [6].

The shape of NMR spectra is significantly influenced by the preference of sub-stitution ions for a particular cationic position. Ions of zinc substitution Zn2+

19

enter in magnetite into A sites, whereas titanium ions Ti4+ occupy B sites. Par-tial replacement of iron ions by ions of the substitution induces a change of thehyperfine field at iron nuclei in the vicinity. If the concentration of substitution islow, satellite structure in 57Fe NMR spectra can be observed. (In case of a higherconcentration of defects, main lines become broader and may overlap the satellitesignals.) Relative intensity of satellite signals is proportional to the substitutionconcentration. The number of satellite lines corresponding to a particular set ofcrystallographically equivalent configurations of resonating nuclei and substituentcan be determined by considering the number of magnetically equivalent configu-rations contained within this set. Crystallographical configurations of a resonatingiron nucleus and a substitution ion in magnetite above the Verwey transition tem-perature are listed in table 3.2 [26]. Rows b) and d) in the table correspond to thezinc substitution, while rows a) and c) apply to the titanium substitution. Figures3.5 and 3.6 displaying the surrounding of the resonating iron nuclei in magnetiteare provided for better understanding.

Table 3.2: Configurations of a resonating iron nucleus and a substitution ion inmagnetite above the Verwey transition temperature [26]List1

Stránka 1

Notation Position of substitution Iron surrounding (within 5 Å)

a) 12 x 3.453 Åb) 4 x 3.607 Åc) 6 x 2.945 Å

d) 6 x 3.453 Å

Position of resonating nucleus

8a = A16d = B8a = A

16d = B16d = B8a = A

In the case noted in table 3.2 as a), the substitution ion is situated in the planeof symmetry for the position of a resonating nucleus and a corresponding tensorof local field anisotropy A has three independent terms α, β and γ:

A =

α β γβ α γγ γ −2α

. (3.1)

The case b) denotes the situation when the substitution ion is located in the planeof symmetry and on the 3-fold axis. The corresponding local field anisotropytensor has only one independent term:

A =

0 γ γγ 0 γγ γ 0

. (3.2)

In the cases c) and d), the substitution is placed in the plane of symmetry for theposition of a resonating nucleus as in the case a). Satellite structure of spectracorresponding to a particular configuration of a resonating iron nucleus and asubstitution ion for a given magnetization direction can be found in table 3.3 [26].

20

Figure 3.5: Surrounding of the resonating iron nucleus at the A site in a puremagnetite (oxygen ions are drawn blue, iron ions at the A sites red and ironions at the B sites green; central ion is highlighted). Created by V. Chlan usingXCrySDen [27].

Figure 3.6: Surrounding of the resonating iron nucleus at the B site in a puremagnetite (oxygen ions are drawn blue, iron ions at the A sites red and ironions at the B sites green; central ion is highlighted). Created by V. Chlan usingXCrySDen [27].

21

Table 3.3: Satellite structure of spectra corresponding to various configurationsof a resonating iron nucleus and a substitution ion in magnetite above the Verweytransition for different magnetization directions [26]List2

Stránka 1

[100]a), c), d) 2 2 : 1

b) 1 I

[110]a), c), d) 4 1 : 1 : 2 : 2

b) 2 1 : 1

[111]a), c), d) 3 1 : 2 : 1

b) 2 1 : 3

Magnetization direction

Notation from the previous

table

Number of

satellites

Ratio of intensities of satellites

Positions of the satellites (in order of the previous

column)

Axx

I + αI – 2α

Axx + Ayy + 2Axy

I + 2α + 2βI + 2α – 2βI – α + 2γI – α – 2γ

I + 2γI – 2γ

2Axy + 2Axz + 2Ayz

I + 2β + 4γI – 2β

I + 2β – 4γI + 6γI – 2γ

∑i , j=1

3

Aijs ni n j

22

Chapter 4

Experiments and Discussion

4.1 Samples

NMR experiments were performed on a series of zinc substituted and titaniumsubstituted magnetite single crystal samples. Chemical formulae of zinc substi-tuted and titanium substituted samples are Fe3−xZnZnxZnO4 and Fe3−xTiTixTiO4,respectively, where the xZn and xTi parameters denote the concentration of sub-stitution. Investigated samples are listed in tables 4.1 and 4.2. Typical dimensionsof samples were of the order of millimeters.

Table 4.1: List of investigated zinc substituted samples

Samplenumber

Samplelabel

Nominalzinc

substitutionxZn

Verweytransitiontempera-

tureTV [K]

Note

Zn1 SM459J#1 0.0075 113.8 small piece cutfrom SM459J

Zn2 SM448#4 0.0086 112.3Zn3 459-1#22

mg30.0174 104.9 xZn according

to electronmicroprobe

measurementin [28]

Samples Ti1 and Ti6 were prepared in the laboratory of professor V. A. M.Brabers at Eindhoven University of Technology using the floating zone method[29]. First of all, stoichiometric polycrystalline rods of desired composition wereprepared using ceramic techniques. These rods were then melted in a floatingzone apparatus, using an arc-image furnace, in a nitrogen atmosphere. Addi-tional annealing in an oxygen atmosphere was performed in order to improve themechanical quality of the crystals.

23

Table 4.2: List of investigated titanium substituted samples

Samplenumber

Samplelabel

Nominaltitanium

substitutionxTi

Verweytransitiontempera-

tureTV [K]

Note

Ti1 Fe2.992Ti0.008O4 0.008 ≈ 116Ti2 392P2#1 0.0065 –

0.0098109 – 116

Ti3 394-1 0.008 – 0.02 < 95Ti4 391P4#1 0.0032 –

0.0040NMR spectrameasured only

at 144 KTi5 447#3A-1 0.01 – 0.026 NMR spectra

measured onlyat 4.2 K

Ti6 S255-4 0.1

All the remaining samples come from the laboratory of Dr. J. Honig at PurdueUniversity, USA [28]. Single crystals were grown from the melt by using the coldcrucible method (skull melter). Subsequently, the crystals were exposed to sub-solidus annealing under CO/CO2 gas mixtures in order to establish the appropriateoxygen stoichiometry, and then quickly quenched to room temperature to freezein the high temperature thermodynamic equilibrium. In spite of the presence ofdefects generated by this procedure, reflecting the high temperature disorder, thesharp transition and the high Verwey transition temperature demonstrate thatmost of the low-temperature electronic processes are not affected.

4.2 Experimental Settings and the Data Pro-

cessing

NMR spectra of 57Fe nuclei were measured in a zero external magnetic field usingthe CPMG pulse sequence. Typical length of π/2-pulse in the pulse sequencewas 1− 2 µs. Typical number of π-pulses (and thus also the number of echoes)was of the order of 10 or 100, as determined by a spin-spin relaxation time andby a time window between π-pulses (= 2tw – see figure 2.2), which was adjustedto values of the order of 10 or 100 µs to accommodate the whole width of theecho. Pulse sequence repetition time (i.e. time between consecutive scans) was inthe range from 5 ms to 6 s, while being set long enough with respect to a spin-lattice relaxation time. The amplitude of RF pulses was properly adjusted beforetaking each spectrum to ensure that only the nuclei in domains would be excited.The chosen number of scans was of the order from 10 to 10,000, depending onthe signal-to-noise ratio. Receiver gain was adjusted to properly utilize the inputrange of the A/D converter. The sample rate of detected signal data was 0.7 or2 MSps and the length of the sampled interval was of the order of 1 or 10 ms,depending on the number of π-pulses and on a width of the time window betweenthem.

24

A wide range of spectra makes it practically impossible to excite the wholespectrum in a single step. Thus, the spectra were acquired step-by-step with atypical frequency step in the range of 30− 75 kHz, depending on the width ofthe spectral lines. Resulting spectra were constructed as an envelope of spectra(Fourier transform modules) corresponding to particular steps – see an illustrationfigure 4.1. In a few cases, the spectra were plotted as Fourier transform modulesat the excitation frequency of particular steps.

64.5 65 65.5 66 66.5

I [a.

u.]

f [MHz]

modules of Fourier transform of particular stepsenvelope of particular Fourier transform modules

Figure 4.1: Illustration of the construction of the spectrum from particular steps(B lines, sample Ti2 at 168 K)

Parameters of subsequent data processing are just as important as the acqui-sition parameters. Employed data processing involves a selection of echoes whichwill be averaged. The first and the second echoes are disqualified as they areusually affected by a higher noise level and by a distorted phase. The choice ofthe last processed echo is limited by a spin-spin relaxation time and by a noiselevel. Comparison of spectra obtained from different rounds of processing withdifferent choices of the last echo provides a qualitative measure of the influence ofa frequency dependence of a spin-spin relaxation time on the shape of the spectra– see figure 4.2. The waveform obtained by the abovementioned averaging con-tains the desired signal in the center and a noise at the sides. Thus, the datapoints containing mostly the noise are cut off to reduce the noise level in a Fouriertransform result. However, the decision about which points belong to noise andwhich still represent the signal depends on the line width and on the intensity ofthe signal of interest. For example, the echo corresponding to a narrow spectralline is broader than an echo belonging to a broad line and thus fewer points canbe discarded than in the latter case. The echo of a weak satellite signal is locatedin a narrow region in the center of the waveform and a noise prevails in the rest,so it may be necessary in some cases to drop a large number of data points inorder to enhance the signal-to-noise ratio of satellite signals in spectrum – the use

25

of this approach in the reported spectra is denoted by an asterisk (”*”) in the key.An illustration is provided in figure 4.3.

64 65 66 67 68 69

I [a.

u.]

f [MHz]

echo 3 - 36 echo 3 - 12

Figure 4.2: Illustrative comparison of spectra based on the same data processedwith different choices of the last echo. The difference between spin-spin relaxationrates of signals at 66.39 MHz and at 68.37 MHz is apparent. (B lines and satellitesignals, sample Ti3 at 128 K)

69 69.5 70 70.5 71 71.5 72

I [a.

u.]

f [MHz]

echo 3 - 51 40x echo 3 - 51 40x * echo 3 - 51

Figure 4.3: Illustration of the effect of discarding data points with prevailingnoise during the data processing – see the text for details (A line and sat 20,sample Zn3 at 106 K)solid line – processing suitable for the main spectral line at 69.73 MHz. Only asmall amount of data points at the sides of a broad echo signal was dropped.dotted line – same as above magnified by a factor of 40dashed line – processing suitable for the weak broad signal at 71.06 MHz. Thesignal-to-noise ratio of this spectral signal was improved by cutting off a largenumber of data points containing mostly the noise at the sides of a weak narrowecho.

26

Several approaches were used to provide the defined temperature during NMRexperiments. During the measurements of spectra at 4.2 K, the probe with thesample was submerged in liquid helium in a Dewar vessel. Several measurementsat 198 K were performed in a mixture of solid carbon dioxide and ethanol in apolystyrene container (temperature deviation was within ±2 K, which was accept-able). The temperature of 273 K was achieved by placing the probe in a mixtureof ice and water in a polystyrene vessel. Spectra were also acquired at the ambi-ent temperature of 299 K. In all the remaining cases, desired temperatures wereprovided by helium continuous flow cryostat.

4.3 Results on Zinc Substituted Magnetite Sam-

ples

4.3.1 Spectra below the Verwey Transition Temperature

NMR spectra of zinc substituted samples Zn1 and Zn2 measured at the tempera-ture of 4.2 K are shown in figures 4.6 and 4.7. There are no significant differencesbetween the spectra of these samples. The structure of the spectra correspondsto the structure of spectra of pure magnetite at this temperature – see figures4.4 and 4.5 for reference. However, the spectral lines are substantially broadeneddue to the presence of the zinc substitution. (See figures 4.3 and 4.4 in [7] forcomparison with spectra of samples with higher concentrations of the zinc sub-stitution.) Typical line widths in spectra of the pure magnetite single crystals at4.2 K are of the order of 10 kHz for A lines and of the order of 10 to 100 kHzfor B lines [2]. The presence of the substitution causes broadening of all spectrallines. Satellite signals cannot be observed as they are overlaid by the dense struc-ture of broadened main lines. The processing of the same experimental data withdifferent numbers of averaged echoes exhibits different spin-spin relaxation ratesof individual spectral lines. Similarly to pure magnetite, the spin-spin relaxationtimes of the B lines are shorter than those of the A lines. However, the relaxationrates in substituted magnetite are generally faster than those in pure magnetite.

48 49 50 51 52

I [a.

u.]

f [MHz]

B lines

Figure 4.4: NMR spectrum of a pure magnetite single crystal at 4.2 K in therange 47.5 – 52.5 MHz (measured by V. Chlan)

27

65 66 67 68 69 70 71 72 73 74 75

I [a.

u.]

f [MHz]

A linesB lines10x

Figure 4.5: NMR spectrum of a pure magnetite single crystal at 4.2 K in therange 65 – 75 MHz (measured by V. Chlan)

48 49 50 51 52

I [a.

u.]

f [MHz]

tw = 22 µs

Zn2 4.2 K echo 3 - 41echo 3 - 9

I [a.

u.]

tw = 67 µs

Zn1 4.2 K echo 3 - 201echo 3 - 34echo 3 - 10

Figure 4.6: Comparison of NMR spectra of zinc substituted samples at 4.2 K inthe range 47.5 – 52.5 MHz (the meaning of tw is illustrated in figure 2.2)

65 66 67 68 69 70 71 72 73 74 75

I [a.

u.]

f [MHz]

tw = 34 µs

Zn2 4.2 K echo 3 - 51echo 3 - 9

I [a.

u.]

tw = 67 µs

Zn1 4.2 K echo 3 - 201echo 3 - 34echo 3 - 10

Figure 4.7: Comparison of NMR spectra of zinc substituted samples at 4.2 K inthe range 65 – 75 MHz

28

4.3.2 Spectra above the Verwey Transition Temperature

Comparisons of NMR spectra of samples Zn1, Zn2 and Zn3 acquired at tempera-tures of 144 K, 216 K and 273 K are depicted in figures 4.10 to 4.15. (Spectra ofsamples with higher concentrations of the zinc substitution at 273 K can be foundin figures 4.9 and 4.10 in [7].) Positions of the main lines in the spectra correspondto those in the spectrum of pure magnetite above the spin reorientation transition– see figures 4.9 and 4.8 for reference. Several satellite signals were observed nearthe B lines and a complex satellite structures were found in the vicinity of the Alines in the spectra of these three samples.

As expected, the sample Zn3, which has the highest substitution concentration,exhibits the broadest spectral lines of these three samples. On the other hand,the lines in the spectra of the sample Zn2 are apparently narrower than thoseof the sample Zn1, which has slightly lower nominal concentration of the zincsubstitution. Deviation of the actual zinc content from the claimed one in one ofthese two samples or the presence of inhomogeneities in the sample Zn1 can beconsidered as the most plausible explanations.

66.5 67 67.5 68 68.5 69 69.5

I [a.

u.]

f [MHz]

A line

20x

Figure 4.8: NMR spectrum of a pure magnetite single crystal at 273 K – A line(measured by V. Chlan)

61 62 63 64 65 66

I [a.

u.]

f [MHz]

20xB lines

B1B2

Figure 4.9: NMR spectrum of a pure magnetite single crystal at 273 K – B lines(measured by V. Chlan)

29

68.5 69 69.5 70 70.5 71

I [a.

u.]

f [MHz]

tw = 47 µs

Zn3 144 K echo 3 - 51

I [a.

u.]

Zn2 144 Kecho 3 - 51 (tw = 367 µs)

15x echo 3 - 51 (tw = 367 µs)echo 3 - 136 (tw = 102 µs)

I [a.

u.]

tw = 62 µs

Zn1 144 K echo 3 - 5115x echo 3 - 51

Figure 4.10: Comparison of NMR spectra of zinc substituted samples at 144 K– A lines

63 64 65 66 67 68 69

I [a.

u.]

f [MHz]

tw = 32 µs

Zn3 144 K echo 3 - 30

I [a.

u.]

tw = 45 µs

Zn2 144 K echo 3 - 315x echo 3 - 31

I [a.

u.]

tw = 32 µs

Zn1 144 K echo 3 - 305x echo 3 - 30

Figure 4.11: Comparison of NMR spectra of zinc substituted samples at 144 K– B lines

30

68 68.5 69 69.5 70 70.5

I [a.

u.]

f [MHz]

tw = 47 µs

Zn3 216 - 217 K echo 3 - 51

I [a.

u.]

Zn2 216.6 K echo 3 - 51 (tw = 367 µs)15x echo 3 - 51 (tw = 367 µs)

10x * echo 3 - 136 (tw = 102 µs)echo 3 - 136 (tw = 102 µs)

I [a.

u.]

tw = 62 µs

Zn1 216 K echo 3 - 5115x echo 3 - 51


62 63 64 65 66 67 68

I [a.

u.]

f [MHz]

tw = 32 µs

Zn3 216 K echo 3 - 305x * echo 3 - 51

I [a.

u.]

tw = 51 µs

Zn2 216.6 K echo 3 - 315x echo 3 - 31

20x * echo 3 - 31

I [a.

u.]

tw = 32 µs

Zn1 216 K echo 3 - 305x echo 3 - 30

20x * echo 3 - 51


31

66.5 67 67.5 68 68.5 69 69.5

I [a.

u.]

f [MHz]

tw = 63 µs

Zn3 273 K echo 3 - 5110x - echo 3 - 51

I [a.

u.]

tw = 307 µs

Zn2 273 K echo 3 - 1715x echo 3 - 17


61 62 63 64 65 66

I [a.

u.]

f [MHz]

tw = 21 µs

Zn3 273 K echo 3 - 51

I [a.

u.]

tw = 57 µs

Zn2 273 K echo 3 - 155x echo 3 - 15


32

4.3.3 Temperature Dependences of Spectra above the Ver-wey Transition Temperature

Temperature dependences of NMR spectra of zinc substituted magnetite samplesZn1, Zn2 and Zn3 were measured from temperatures slightly above the Verweytransition up to 299 K. The acquired spectra are plotted in figures A.1 to A.9in Appendix, while figures 4.16 to 4.21 show the spectra plotted relative to themost intensive line in the displayed spectral range, thus making it easier to qual-itatively evaluate the temperature evolution of relative position, line width andshape of spectral signals. In accordance with the fact that the Verwey transitiontemperature decreases with increasing concentration of substitution and defects(see figure 3.4), spectra corresponding to a cubic phase were observed to lowertemperatures compared to pure magnetite (≈ 115 K for samples Zn1 and Zn2,≈ 106 K for sample Zn3). The most apparent changes in the spectra are the spinreorientation transition and the narrowing of the main lines with the increasingtemperature. Special care was taken to find the satellite lines in the spectra inorder to be able to track the variation of their frequencies against the temperature.

33

-1 -0.5 0 0.5 1 1.5 2

I [a.

u.]

∆f [MHz]

tw = 47 µs115.7 - 115.3 K

sat 20

echo 3 - 5115x echo 3 - 51

I [a.

u.]

tw = 47 µs120 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 47 µs124 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 47 µs128.0 - 127.4 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 62 µs144 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 62 µs168 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 62 µs198 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 62 µs216 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 77 µs237.0 - 237.3 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 97 µs299 K echo 3 - 101

15x echo 3 - 101

Figure 4.16: Temperature dependence of NMR spectra of sample Zn1 – spectraplotted relative to the A lines

34

-3 -2 -1 0 1 2 3

I [a.

u.]

∆f [MHz]

tw = 32 µs115.7 K echo 3 - 30

5x echo 3 - 30

I [a.

u.]

tw = 32 µs120 K echo 3 - 30

5x echo 3 - 30

I [a.

u.]

tw = 32 µs124 K echo 3 - 30

5x echo 3 - 30

I [a.

u.]

tw = 32 µs128 K echo 3 - 30

5x echo 3 - 3020x * echo 3 - 51

I [a.

u.]

tw = 32 µs144 K echo 3 - 30

5x echo 3 - 30

I [a.

u.]

tw = 32 µs168 K echo 3 - 30

5x echo 3 - 3020x * echo 3 - 51

I [a.

u.]

tw = 32 µs198 K echo 3 - 30

5x echo 3 - 3020x * echo 3 - 51

I [a.

u.]

tw = 32 µs216 K

sat 1sat 2 sat 3

sat 4

sat 5 echo 3 - 305x echo 3 - 30

20x * echo 3 - 51

I [a.

u.]

tw = 32 µs237 K echo 3 - 30

5x echo 3 - 3020x * echo 3 - 51

I [a.

u.] tw = 23 µs299 K echo 3 - 43

5x echo 3 - 4320x echo 3 - 81

Figure 4.17: Temperature dependence of NMR spectra of sample Zn1 – spectraplotted relative to the B, B2 lines

35

-1 -0.5 0 0.5 1 1.5 2

I [a.

u.]

∆f [MHz]

114.6 K echo 3 - 51 (tw = 257 µs)15x echo 3 - 51 (tw = 257 µs)60x echo 3 - 51 (tw = 57 µs)

I [a.

u.]

tw = 257 µs118.5 K

sat 20

echo 3 - 4115x echo 3 - 41

100x * echo 3 - 12

I [a.

u.] 123.4 K echo 3 - 51 (tw = 257 µs)

15x echo 3 - 51 (tw = 257 µs)150x echo 3 - 51 (tw = 57 µs)

I [a.

u.] 130.5 K echo 3 - 51 (tw = 367 µs)

15x echo 3 - 51 (tw = 367 µs)200x * echo 3 - 136 (tw = 102 µs)

75x echo 3 - 136 (tw = 102 µs)

I [a.

u.] 144 K echo 3 - 51 (tw = 367 µs)


50x echo 3 - 136 (tw = 102 µs)

I [a.

u.] 167.5 K echo 3 - 51 (tw = 367 µs)


60x echo 3 - 136 (tw = 102 µs)

I [a.

u.]

tw = 263 µs

198 KCO2(s)/C2H5OH(l)

echo 3 - 91echo 3 - 20

15x echo 3 - 9115x echo 3 - 20

I [a.

u.] 216.6 K echo 3 - 51 (tw = 367 µs)


50x echo 3 - 136 (tw = 102 µs)

I [a.

u.] 240.5 K

sat. 240.5 - 235.0 K

echo 3 - 51 (tw = 367 µs)15x echo 3 - 51 (tw = 367 µs)

150x * echo 3 - 136 (tw = 102 µs)40x echo 3 - 136 (tw = 102 µs)

I [a.

u.]

tw = 307 µs273 K echo 3 - 17

15x echo 3 - 17

I [a.

u.]

tw = 344 µs299 K echo 3 - 41

15x echo 3 - 41


36

-3 -2 -1 0 1 2 3

I [a.

u.]

∆f [MHz]

tw = 45 µs114.6 K echo 3 - 25

5x echo 3 - 25

I [a.

u.]

tw = 45 µs118.6 K echo 3 - 31

5x echo 3 - 31

I [a.

u.]

tw = 45 µs123.3 K echo 3 - 31

5x echo 3 - 31

I [a.

u.]

tw = 51 µs130.5 K echo 3 - 31

5x echo 3 - 31

I [a.

u.]

tw = 45 µs144 K echo 3 - 31

5x echo 3 - 31

I [a.

u.]

tw = 51 µs167.4 K echo 3 - 31

5x echo 3 - 3120x * echo 3 - 19

I [a.

u.]

tw = 61 µs


echo 3 - 505x echo 3 - 50

I [a.

u.]

tw = 51 µs216.6 K

sat 1sat 2

sat 3 sat 5 echo 3 - 315x echo 3 - 31

20x * echo 3 - 31

I [a.

u.]

tw = 51 µs240.5 K echo 3 - 31

5x echo 3 - 3120x * echo 3 - 31

I [a.

u.]

tw = 57 µs273 K echo 3 - 15

5x echo 3 - 15

I [a.

u.]

tw = 62 µs299 K echo 3 - 37

5x echo 3 - 37


37

-1 -0.5 0 0.5 1 1.5 2

I [a.

u.]

∆f [MHz]

tw = 47 µs

106 K

sat 20

echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

128 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

144 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

168 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

197 - 198 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

216 - 217 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

237 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 63 µs

273 K echo 3 - 5110x - echo 3 - 51

I [a.

u.] tw = 344 µs299 K echo 3 - 31

40x * echo 3 - 31


38

-3 -2 -1 0 1 2 3

I [a.

u.]

∆f [MHz]

tw = 32 µs

106 K echo 3 - 12

I [a.

u.]

tw = 32 µs

128 K echo 3 - 30

I [a.

u.]

tw = 32 µs

144 K echo 3 - 30

I [a.

u.]

tw = 32 µs

168 K echo 3 - 305x * echo 3 - 51

I [a.

u.]

tw = 32 µs

197.5 K echo 3 - 30

I [a.

u.]

tw = 32 µs

216 K echo 3 - 305x * echo 3 - 51

I [a.

u.]

tw = 32 µs

237.3 K echo 3 - 305x * echo 3 - 51

I [a.

u.]

tw = 21 µs

273 K echo 3 - 51

I [a.

u.]

tw = 47 µs

299 K

sat 1sat 3 sat 5

echo 3 - 41


39

4.3.4 Temperature Dependences of Spectral Signal Fre-quencies

The results of the measurements of the temperature dependences of spectra wereused to find the positions of the main lines and of the satellite signals in order toconstruct the temperature dependences of their frequencies. Assembled data canbe found in tables B.1 to B.6 in Appendix, while the graphical representation isshown in figure 4.22.

Several satellite lines found near the B lines probably arise from the presenceof a zinc ion Zn2+ in the A position nearest to the resonating nuclei at the Bsites. A complex satellite pattern in the vicinity of the A line is localized closeto the main line because the distance between the substitution at the A site andthe resonating nuclei at the A sites is higher and thus the corresponding changeof the hyperfine field is lower. A high number of satellite lines in this patternindicates that many of these signals are induced by the substitution in the distantsurrounding of the resonating nuclei.

Satellite signals in the spectra of the sample Zn2 which are denoted in tableB.4 by an asterisk (”*”) were not found in the spectra of the other zinc substitutedmagnetite samples. However, these signals coincide with the satellite lines in thespectra of the non-stoichiometric magnetite reported in [22] – see figure 4.23.Thus the presence of vacancies in the sample is evidenced. Concentration of thevacancies is of the order of 10−4 vacancies per formula unit, as estimated fromintensities of the corresponding satellite signals.

40

61

62

63

64

65

66

67

68

69

70

71

72

73

74

100 150 200 250 300

f [M

Hz]

T [K]

sat 1

sat 2 sat 3

sat 4

sat 5

sat 20

main lines Zn1satellites Zn1


satellites - vacancies Zn2


Figure 4.22: Temperature dependences of frequencies of the main lines and ofthe satellite signals in the spectra of the zinc substituted samples

41

67

68

69

70

71

72

73

74

100 150 200 250 300

f [M

Hz]

T [K]

A line non-stoichiometric magnetitesatellites non-stoichiometric magnetite

A line Zn2satellites - vacancies Zn2

Figure 4.23: Comparison of the temperature dependences of frequencies of theA line and of the satellite signals corresponding to the presence of vacancies inthe spectra of the sample Zn2 with the data for non-stoichiometric magnetiteFe3(1−0.0025)O4 [22]

42

4.3.5 Temperature Dependences of HWHM of the A Lines

The half widths of the A lines in the temperature dependences of the spectraof the samples Zn1, Zn2 and Zn3 are listed in tables C.1 to C.3 in Appendix.The variation of HWHM of the A lines against the temperature is plotted infigure 4.24. Significant differences between the curves for particular samples canbe clearly seen: especially the curve for the sample Zn2 suggests lower actualconcentration of the zinc substitution than the nominal one.

0

10

20

30

40

50

60

70

80

90

100 150 200 250 300

HW

HM

[kH

z]

T [K]

Zn1 Zn2 Zn3

Figure 4.24: Temperature dependences of half width at half maximum of the Alines in the spectra of the zinc substituted samples

4.4 Results on Titanium Substituted Magnetite

Samples

4.4.1 Spectra below the Verwey Transition Temperature

Spectra of titanium substituted samples Ti1, Ti5 and Ti6 acquired at 4.2 K arepresented in figures 4.25 and 4.26. Just like in the case of the zinc substitutedsamples, the structure of the spectra matches the structure of the spectra of puremagnetite at the same temperature (see figures 4.6 and 4.7). The presence oftitanium substitution causes a broadening of the spectral lines, especially in thespectrum of the sample Ti6, which has relatively high substitution concentration.Satellite signals are overlaid by the dense structure of broadened main lines andthus they cannot be observed.

43

48 49 50 51 52

I [a.

u.]

f [MHz]

tw = 67 µs

Ti5 4.2 K echo 3 - 201echo 3 - 34echo 3 - 10

I [a.

u.]

tw = 47 µs


Figure 4.25: Comparison of NMR spectra of titanium substituted samples at4.2 K in the range 47.5 – 52.5 MHz

65 66 67 68 69 70 71 72 73 74 75

I [a.

u.]

f [MHz]

tw = 35 µs

Ti6 4.2 K

I [a.

u.]

tw = 67 µs


I [a.

u.]

tw = 47 µs


Figure 4.26: Comparison of NMR spectra of titanium substituted samples at4.2 K in the range 65 – 75 MHz

44

4.4.2 Spectra above the Verwey Transition Temperature

NMR spectra of samples Ti1, Ti2, Ti3, Ti4 and Ti6 measured at temperatures of144 K, 237 K and 273 K are compared in figures 4.27 to 4.32. Similarly to thespectra of the zinc substituted samples, the main spectral lines correspond to thosein the spectrum of pure magnetite above the spin reorientation transition. In thespectra of the samples Ti1, Ti2, Ti3 and Ti4, satellite patterns were observed inthe neighbourhood of the A lines, several satellite signals were resolved close tothe B lines (except the sample Ti4 measured only at 144 K) and satellite lineswere also evidenced in the region between the B and the A lines (this is also thecase of the sample Ti6).

The spectra of the sample Ti6 are composed of relatively broad lines due tothe high concentration of titanium substitution, whereas the spectral lines of thesample Ti4, which has the lowest titanium content, are the narrowest of all thesesamples. The widths of lines in the spectrum of the sample Ti2 are slightly higherthan those of the sample Ti4 but still lower than those of the sample Ti1, thussuggesting that the actual substitution concentration is in the lower end of theclaimed range. The line widths in the case of the sample Ti3 are apparently higherthan those of the sample Ti1, so the titanium content at the higher end of theprovided range of nominal substitution can be expected.

67 68 69 70 71 72

I [a.

u.]

f [MHz]

tw = 47 µsTi4 144 K echo 3 - 301

echo 3 - 51250x satellites - echo 3 - 301

I [a.

u.]

tw = 67 µs

Ti3 144 K echo 3 - 134echo 3 - 34

15x echo 3 - 134

I [a.

u.]

tw = 67 µs

Ti2 144 K echo 3 - 301echo 3 - 36

100x echo 3 - 201

I [a.

u.]

tw = 47 µs

Ti1 144 K echo 3 - 201echo 3 - 51

30x * echo 3 - 201

Figure 4.27: Comparison of NMR spectra of titanium substituted samples at144 K – A lines

45

63 64 65 66 67 68 69

I [a.

u.]

f [MHz]

tw = 19 µs

Ti4 144 K echo 3 - 51echo 3 - 12

I [a.

u.]

tw = 19 µs

Ti3 144 K echo 3 - 81echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

Ti2 144 K echo 3 - 81echo 3 - 51echo 3 - 36echo 3 - 12

10x echo 3 - 81

I [a.

u.]

tw = 19 µs

Ti1 144 K echo 3 - 36echo 3 - 12

5x echo 3 - 36

Figure 4.28: Comparison of NMR spectra of titanium substituted samples at144 K – B lines

66 67 68 69 70 71

I [a.

u.]

f [MHz]

tw = 97 µs

Ti3 237 K echo 3 - 91echo 3 - 23

15x echo 3 - 91

I [a.

u.]

Ti2 236.3 - 237.0 K echo 3 - 151 (tw = 97 µs)echo 3 - 26 (tw = 97 µs)


I [a.

u.]

tw = 97 µs

Ti1 237 K echo 3 - 91echo 3 - 23

30x * echo 3 - 91


46

62 63 64 65 66 67 68

I [a.

u.]

f [MHz]

tw = 97 µs


I [a.

u.]

tw = 23 µs

Ti2 236.7 - 236.4 K echo 3 - 81echo 3 - 66echo 3 - 30echo 3 - 10

10x echo 3 - 81

I [a.

u.]

tw = 23 µs


5x echo 3 - 81


65 66 67 68 69 70

I [a.

u.]

f [MHz]

tw = 21 µs

Ti6 273 K

I [a.

u.]

tw = 77 µs

Ti1 273 K echo 3 - 51echo 3 - 29

30x * echo 3 - 51


47

61 62 63 64 65 66 67

I [a.

u.]

f [MHz]

tw = 21 µs

Ti6 273 K

I [a.

u.]

tw = 77 µs

Ti1 273 K echo 3 - 24echo 3 - 20echo 3 - 9

5x echo 3 - 24


4.4.3 Temperature Dependences of Spectra above the Ver-wey Transition Temperature

Variation of NMR spectra of titanium substituted magnetite samples Ti1, Ti2 andTi3 against the temperature were measured from temperatures near the Verweytransition up to 299 K. The obtained spectra are displayed in figures D.1 to D.9in Appendix. In order to simplify a qualitative evaluation of the changes in thespectra with the varying temperature, the spectra were plotted relative to themost intensive line in the spectral range shown in figures 4.33 to 4.38. Graphsin the figures D.1 to D.9 which evidently belong to the temperatures when thesamples were slightly below the Verwey transition are not given here. The mostobvious effect in the spectra is presented by the spin reorientation transition.Furthermore, the narrowing of the main lines with the increasing temperaturewas observed. Just like in the case of the zinc substituted samples, particularcare was taken to detect the satellite lines in the spectra to be able to track thedependences of their frequencies on the temperature.

48

-2 -1 0 1 2

I [a.

u.]

∆f [MHz]

tw = 47 µs116 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs116.5 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs119 - 117 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs124 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs128 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs136 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs144 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 67 µs168 K echo 3 - 134

echo 3 - 3430x * echo 3 - 134

I [a.

u.]

tw = 67 µs198 K echo 3 - 134

echo 3 - 3430x * echo 3 - 134

I [a.

u.]

tw = 67 µs216 - 215.4 K echo 3 - 134

echo 3 - 3430x * echo 3 - 134

I [a.

u.]

tw = 97 µs237 K echo 3 - 91

echo 3 - 2330x * echo 3 - 91

I [a.

u.]

tw = 77 µs273 K echo 3 - 51

echo 3 - 2930x * echo 3 - 51

I [a.

u.]

tw = 97 µs299 K

sat 5sat 6

sat 7echo 3 - 91echo 3 - 23

30x echo 3 - 9130x satellites - echo 3 - 151

Figure 4.33: Temperature dependence of NMR spectra of sample Ti1 – spectraplotted relative to the A lines. The trace of low-temperature phase lines is visiblein the spectrum at 116 K (marked by a light blue rectangle).

49

-3 -2 -1 0 1 2 3

I [a.

u.]

∆f [MHz]

tw = 19 µs116 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs116.5 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs118 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs124 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs128 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs136 K echo 3 - 36

echo 3 - 125x echo 3 - 36

I [a.

u.]

tw = 19 µs144 K echo 3 - 36

echo 3 - 125x echo 3 - 36

I [a.

u.]

tw = 19 µs168 K echo 3 - 81

echo 3 - 36echo 3 - 12

5x echo 3 - 81

I [a.

u.]

tw = 19 µs198 K echo 3 - 81

echo 3 - 36echo 3 - 12

5x echo 3 - 81

I [a.

u.]

tw = 19 µs216 K echo 3 - 81

echo 3 - 36echo 3 - 12

5x echo 3 - 81

I [a.

u.]

tw = 23 µs237 K echo 3 - 81

echo 3 - 66echo 3 - 30

echo 3 - 105x echo 3 - 81

I [a.

u.]

tw = 77 µs273 K echo 3 - 24

echo 3 - 20echo 3 - 9

5x echo 3 - 24

I [a.

u.]

tw = 23 µs299 K

sat 2 sat 4echo 3 - 81echo 3 - 66echo 3 - 30

echo 3 - 105x echo 3 - 81

Figure 4.34: Temperature dependence of NMR spectra of sample Ti1 – spectraplotted relative to the B, B2 lines

50

-2 -1 0 1 2

I [a.

u.]

∆f [MHz]

tw = 47 µs

115.7 - 116.6 K echo 3 - 301echo 3 - 51

100x echo 3 - 301

I [a.

u.]

tw = 47 µs

124.0 - 123.5 K echo 3 - 301echo 3 - 51

100x echo 3 - 301

I [a.

u.]

tw = 47 µs

128.0 - 127.3 K echo 3 - 301echo 3 - 51

100x echo 3 - 301

I [a.

u.]

tw = 67 µs

144 K echo 3 - 301echo 3 - 36

100x echo 3 - 201

I [a.

u.]

tw = 67 µs

168 K echo 3 - 301echo 3 - 36

100x echo 3 - 201

I [a.

u.]

tw = 67 µs

198 K echo 3 - 301echo 3 - 36

100x echo 3 - 201

I [a.

u.] 236.3 - 237.0 K echo 3 - 151 (tw = 97 µs)


100x * echo 3 - 301 (tw = 47 µs)

I [a.

u.]

tw = 97 µs

298 K

sat 5sat 6

sat 7

echo 3 - 151echo 3 - 26

100x echo 3 - 151100x * echo 3 - 100

Figure 4.35: Temperature dependence of NMR spectra of sample Ti2 – spectraplotted relative to the A lines

51

-3 -2 -1 0 1 2 3

I [a.

u.]

∆f [MHz]

tw = 19 µs

116 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

124 K echo 3 - 51echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

128 K echo 3 - 51echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

144 K echo 3 - 81echo 3 - 51echo 3 - 36

echo 3 - 1210x echo 3 - 81

I [a.

u.]

tw = 19 µs

168 K echo 3 - 81echo 3 - 51echo 3 - 36

echo 3 - 1210x echo 3 - 81

I [a.

u.]

tw = 19 µs

198.0 - 198.4 K echo 3 - 81echo 3 - 51echo 3 - 36

echo 3 - 1210x echo 3 - 81

I [a.

u.]

tw = 23 µs

236.7 - 236.4 K sat 1

sat 2

sat 3

sat 4

echo 3 - 81echo 3 - 66echo 3 - 30

echo 3 - 1010x echo 3 - 81

I [a.

u.]

tw = 23 µs

298.7 - 299.5 K echo 3 - 81echo 3 - 66echo 3 - 30

echo 3 - 1010x echo 3 - 81


52

-2 -1 0 1 2

I [a.

u.]

∆f [MHz]

tw = 47 µs

95 K echo 3 - 201echo 3 - 51

15x echo 3 - 201

I [a.

u.]

tw = 47 µs

109.0 - 108.2 K echo 3 - 201echo 3 - 51

15x echo 3 - 201

I [a.

u.]

tw = 47 µs

124.0 - 122.3 K echo 3 - 201echo 3 - 51

15x echo 3 - 201

I [a.

u.]

tw = 47 µs

128.0 - 128.5 K echo 3 - 201echo 3 - 51

15x echo 3 - 201

I [a.

u.]

tw = 67 µs

144 K echo 3 - 134echo 3 - 34

15x echo 3 - 134

I [a.

u.]

tw = 67 µs

198 K echo 3 - 134echo 3 - 34

15x echo 3 - 134

I [a.

u.]

tw = 97 µs

237 Ksat 6 sat 7

echo 3 - 91echo 3 - 23

15x echo 3 - 91

I [a.

u.]

tw = 97 µs

299 K echo 3 - 91echo 3 - 23

15x echo 3 - 91

Figure 4.37: Temperature dependence of NMR spectra of sample Ti3 – spectraplotted relative to the A lines

53

-3 -2 -1 0 1 2 3

I [a.

u.]

∆f [MHz]

tw = 19 µs

95.0 - 95.6 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

109 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

124 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

128 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

144 K echo 3 - 81echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

198 K echo 3 - 81echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 97 µs

237 K echo 3 - 81echo 3 - 66echo 3 - 30echo 3 - 10

I [a.

u.]

tw = 97 µs

299.4 K

sat 2 sat 4

echo 3 - 81echo 3 - 66echo 3 - 30echo 3 - 10


54

4.4.4 Temperature Dependences of Spectral Signal Fre-quencies

The frequencies of the main lines and of the satellite signals found in the tempera-ture dependences of spectra are listed in tables E.1 to E.6 in Appendix and a graphof these temperature dependences is presented in figure 4.39. Satellite signals sat5, sat 6 and sat 7 located in between the A line and the B lines originate from thepresence of the titanium ion Ti4+ at the B site nearest to the resonating nucleiat the A sites, whereas the satellite pattern in the vicinity of the A line probablycomes from the presence of the substitution at the B site in wider surroundingsof the resonating nuclei at the A sites. Satellite lines sat 2 and sat 4 near theB lines arise from the resonating nuclei at the B sites with the substitution atthe B site in the vicinity. The splitting between the B lines and these satellitesis lower than that between the A line and the satellites sat 5, sat 6 and sat 7due to higher distance between the nearest B sites than between the nearest Aand B sites. Satellites sat 1 and sat 3 probably correspond to the presence of thetitanium ion Ti4+ in a more distant neighbourhood of the resonating nuclei at theB sites.

55

62

63

64

65

66

67

68

69

70

71

100 150 200 250 300

f [M

Hz]

T [K]

sat 1

sat 2

sat 3

sat 4

sat 5, 6

sat 7

main lines Ti1satellites Ti1



Figure 4.39: Temperature dependences of frequencies of the main lines and ofthe satellite signals in the spectra of the titanium substituted samples

56

4.4.5 Temperature Dependences of HWHM of the A Lines

The half widths of the A lines read out from the temperature dependences ofthe spectra of the samples Ti1, Ti2 and Ti3 are given in tables F.1 to F.3 inAppendix. Graphical representation of the variation of HWHM of the A linesagainst the temperature is provided in figure 4.40. The differences between curvesare apparent, particularly interesting is the slightly faster decay of the dependencefor the sample Ti2 than for the sample Ti1, supporting the suggestion of the actualconcentration of the substitution in the sample Ti2 being near the lower end ofthe claimed range.

0

20

40

60

80

100

120

140

100 150 200 250 300

HW

HM

[kH

z]

T [K]

Ti1 Ti2 Ti3

Figure 4.40: Temperature dependences of half width at half maximum of the Alines in the spectra of the titanium substituted samples

4.5 Discussion

Analysis of the acquired NMR spectra of the zinc and titanium substituted mag-netite is based on an interpretation of spectra of pure magnetite at the correspond-ing temperature. In addition to giving rise to satellite signals, the presence of thesubstitution causes broadening of lines in the spectra.

Experiments at 4.2 K were performed on samples with relatively low substitu-tion concentration except the sample Ti6, thus it is possible to distinguish mostof the spectral lines despite their broadening. Frequencies of the spectral linesare the same as those of the lines in the spectra of pure magnetite. However, asalready stated, the satellite pattern could not be observed due to being overlaidby the dense structure of the broadened main lines. In case of the sample Ti6, thelines in the spectra are so broad that it is impossible to resolve particular lines.

The structure of the main lines in the spectra acquired at the temperaturesabove the Verwey transition is relatively simple and the frequencies of the main

57

lines correspond to those of the lines in the spectra of pure magnetite – see figure4.41. The most apparent effect in the spectra is the spin reorientation transitionmanifesting itself by the splitting of the B line into the B1 and B2 lines. The spectracorresponding to a cubic phase were observed to lower temperatures compared topure magnetite because the Verwey transition temperatures of the investigatedsamples are lower due to the presence of the substitution. The spectrum of thesample Ti6 at 273 K differs from the spectra of the other titanium substitutedsamples by significantly broader lines making the B lines merge into a wide band,by the lower frequency of the A line and by a high intensity of the satellite signalbetween the A and B lines due to relatively high substitution concentration.

62

63

64

65

66

67

68

69

70

100 150 200 250 300

f [M

Hz]

T [K]

Ti1Ti2Ti3Zn1

Zn2Zn3

pure magnetite above TVpure magnetite below TV

Figure 4.41: Temperature dependences of frequencies of the main lines in thespectra of the zinc and titanium substituted samples and of pure magnetite [26],[3]

58

Satellite signal patterns were observed in the spectra measured above the Ver-wey transition frequency and the temperature dependences of their frequencieswere constructed. The limitation factors of resolving the satellite signals were thesignal-to-noise ratio and the overlaying of the satellites by the broadened mainspectral lines in case of the satellite lines that were located close to the main lines.

In case of the zinc substituted samples, there are numerous satellite lines closeto the A line, forming a complex structure arising from the presence of zinc ionZn2+ in a wider surrounding of the resonating nuclei at the A site. There were alsoseveral satellite lines resolved in the vicinity of the B lines. Satellite sat 1 and mostlikely also satellites sat 3 and sat 5 originate from the presence of the substitutionin the A position nearest to the resonating nuclei at the B sites, whereas in caseof the satellite signals sat 2 and sat 4, we cannot avoid the possibility that thesesignals are caused be the zinc ion Zn2+ located at the A site in a more distantsurrounding of the resonating nuclei at the B positions. Temperature dependencesof frequencies of the satellite lines plotted relative to the main lines are presentedin figures 4.42 and 4.43. Satellite line sat 1, which is of a particular interest due tothe highest splitting between this line and the B lines, was compared in figure 4.44to the satellite observed below the B lines in the spectra of gallium substitutedmagnetite [30]. Temperature dependences of frequencies of the satellite signal sat1and of the B2 line normalized to their frequencies at 299 K are shown in figure 4.45and a similar plot in figure 4.46 provides the comparison with the abovementionedsatellite found in the spectra of gallium substituted magnetite. As evidenced, adecrease of the frequency with increasing temperature of the satellite sat 1 ismuch slower than in case of the referred satellite line in the spectra of galliumsubstituted magnetite. Another signal deserving a special mention is marked assat 20. Origin of this relatively broad line, which was observed only at the lowerend of the temperature dependences, is not clear – it may be a satellite signal fromresonating iron nuclei at the A sites but it can also be caused by the resonanceof the oxygen nuclei 17O reported in [31] at about 80 MHz for the (Zn-Mn-Fe)O4

compound at the temperature of 4 K. Satellite signals observed in the spectraof the sample Zn2 which are marked in table B.4 by an asterisk originate fromthe presence of a low concentration of vacancies in the sample, as was clearlydemonstrated in figure 4.23.

The most interesting satellite signals found in the spectra of the titaniumsubstituted samples, marked sat 5, sat 6 and sat 7, are in between the A line andthe B lines. At higher temperatures, these signals can be resolved as three distinctlines with intensity ratio of 1:1:2 (see table 3.3). These satellite lines arise from thepresence of the substitution at the B site nearest to the resonating nuclei at theA sites. The satellite lines near the A line probably originate from the presence ofthe titanium ion Ti4+ at B site in wider neighbourhood of the resonating nucleiat the A sites. Satellite lines in the vicinity of the B lines can be divided intotwo groups. The first group consisting of the satellites sat 2 and sat 4 arise fromthe presence of the substitution at the B site nearest to the resonating nuclei atthe B sites. The second group is formed by the satellite signals sat 1 and sat 3induced probably by the substitution ion located in a wider surroundings of theresonating nuclei at the B sites. Temperature dependences of frequencies of thesatellite lines plotted relative to the main lines are provided in figures 4.47 and4.48. Temperature dependences of frequencies of the satellite signals sat 5, sat 6

59

-0.5

0

0.5

1

1.5

100 150 200 250 300

∆f [M

Hz]

T [K]

Zn1 Zn2 Zn3

Figure 4.42: Temperature dependences of frequencies of the satellite signals nearthe A line in the spectra of the zinc substituted samples plotted relative to the Aline

60

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

100 150 200 250 300

∆f [M

Hz]

T [K]B1 line Zn1

satellites Zn1B1 line Zn2

satellites Zn2B1 line Zn3

satellites Zn3

Figure 4.43: Temperature dependences of frequencies of the B1 line and thesatellite signals near the B lines in the spectra of the zinc substituted samplesplotted relative to the B2 line

61

60

61

62

63

64

65

66

67

100 150 200 250 300

f [M

Hz]

T [K]




main lines - Ga substituted magnetitesatellites - Ga substituted magnetite

Figure 4.44: Comparison of the temperature dependences of frequencies of theB lines and of the satellite signals near them in the spectra of the zinc substitutedsamples with the data for gallium substituted magnetite Fe2.95Ga0.05O4 [30]

62

0.995

1

1.005

1.01

1.015

1.02

1.025

1.03

1.035

1.04

1.045

1.05

100 150 200 250 300

f / f 2

99 K

T [K]B2 line Zn1

sat 1 Zn1B2 line Zn2


sat 1 Zn3

Figure 4.45: Temperature dependences of frequencies of the B2 line and of thesatellite signal sat1 in the spectra of the zinc substituted samples normalized totheir frequencies at 299 K

63

0.995

1

1.005

1.01

1.015

1.02

1.025

1.03

1.035

1.04

1.045

1.05

100 150 200 250 300

f / f 2

99 K

T [K]B2 line Zn1



sat 1 Zn3B2 line Ga substituted magnetite

satellite Ga substituted magnetite

Figure 4.46: Comparison of the temperature dependences of frequencies of the B2

line and of the satellite signal sat1 in the spectra of the zinc substituted samplesnormalized to their frequencies at 299 K with the data for gallium substitutedmagnetite Fe2.95Ga0.05O4 [30]

64

and sat 7 and of the A line normalized to their frequencies at 144 K is presented infigure 4.49 and the comparison with the satellite signal in the spectra of aluminiumsubstituted magnetite [3] and of non-stoichiometric magnetite [22] is provided infigure 4.50. A decrease of the frequency with increasing temperature of the satellitesignals sat 5, sat 6 and sat 7 is slower than in case of the satellites in the spectraof non-stoichiometric magnetite but it is faster than in case of satellite lines in thespectra of aluminium substituted magnetite. However, all displayed satellite lineshave faster decrease of the frequency with increasing temperature than the mainA line due to a perturbed A-B exchange interaction.

-2

-1.5

-1

-0.5

0

0.5

1

100 150 200 250 300

∆f [M

Hz]

T [K]

Ti1 Ti2 Ti3

Figure 4.47: Temperature dependences of frequencies of the satellite signals nearthe A line in the spectra of the titanium substituted samples plotted relative tothe A line

Temperature dependences of the widths of the A lines in the acquired spec-tra above the Verwey transition exhibit very interesting behaviour. Typically in

65

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

100 150 200 250 300

∆f [M

Hz]

T [K]B1 line Ti1

satellites Ti1B1 line Ti2

satellites Ti2B1 line Ti3

satellites Ti3

Figure 4.48: Temperature dependences of frequencies of the B1 line and thesatellite signals near the B lines in the spectra of the titanium substituted samplesplotted relative to the B2 line

66

0.96

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

1.01

100 150 200 250 300

f / f 1

44 K

T [K]

A line Ti1sat 5 Ti1sat 6 Ti1sat 7 Ti1


A line Ti3sat 6 Ti3sat 7 Ti3

Figure 4.49: Temperature dependences of frequencies of the A line and of thesatellite signals sat 5, sat 6 and sat 7 in the spectra of the titanium substitutedsamples normalized to their frequencies at 144 K

67

0.96

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

1.01

100 150 200 250 300

f / f 1

44 K

T [K]



A line Ti3sat 6 Ti3sat 7 Ti3

A line Al substituted magnetitesatellites Al substituted magnetite

A line non-stoichiometric magnetitesatellites non-stoichiometric magnetite

Figure 4.50: Comparison of the temperature dependences of frequencies of theA line and of the satellite signal sat1 in the spectra of the titanium substitutedsamples normalized to their frequencies at 144 K with the data for aluminiumsubstituted magnetite Fe2.995Al0.005O4 [3] and for non-stoichiometric magnetiteFe3(1−0.0025)O4 [22]

68

magnetic iron oxides, the line widths increase with increasing temperature dueto the increasing fluctuations of the hyperfine magnetic field – a model case isrepresented by the spectral lines of YIG (see [32]). However, as shown in [23],the A line in the spectra of pure magnetite is broadened at temperatures near thespin reorientation transition and quickly decreases with the increasing tempera-ture up to approximately 260 K and then increases at higher temperatures. Thepresence of the substitution or vacancies in the sample broadens the widths of thespectral lines and emphasizes the effect of the decrease in the A line width withincreasing temperature. Comparison of the temperature dependences of widths ofthe A lines obtained from the measured temperature dependences of the spectraof the zinc and titanium samples with the data for pure magnetite [3], [23] andthe magnetite samples with aluminium substitution [3] and with vacancies [22]is provided in figure 4.51. The A line width in the spectra of the sample Zn2above the spin reorientation transition is relatively close to the width of the A lineof pure magnetite. However, the line width sharply increases when the temper-ature decreases toward the Verwey transition, which might be explained by theincreasing disorder in the electron system enhanced by the presence of the zincsubstitution. All the remaining dependences presented in figure 4.51 exhibit Aline widths significantly higher than those in the spectra of pure magnetite, andalthough the ratio of the line width near the Verwey transition and that at theambient temperature is higher than in case of pure magnetite, the decrease of theline width with increasing temperature is considerably slower than in case of thesample Zn2. Moreover, the decay of the A line width in these cases does not seemto be tightly connected with the spin reorientation transition. A possible expla-nation can be found in an idea that with decreasing temperature the presence ofthe substitution or vacancies in the sample increasingly affects electron dynamicsin the sample thus producing inhomogeneities of the electron density, resulting ina broader hyperfine field distribution.

69

0

20

40

60

80

100

120

100 150 200 250 300

HW

HM

[kH

z]

T [K]Al substituted magnetite Fe2.995Al0.005O4

Al substituted magnetite Fe2.97Al0.03O4non-stoichiometric magnetite Fe3(1-0.0025)O4non-stoichiometric magnetite Fe3(1-0.0090)O4

pure magnetite

Zn1Zn2Zn3Ti1Ti2Ti3

Figure 4.51: Comparison of the temperature dependences of half width at halfmaximum of the A lines in the spectra of aluminium substituted samples [3], non-stoichiometric magnetite [22], pure magnetite [3], [23] and the zinc and titaniumsubstituted samples

70

Chapter 5

Conclusion

The subject matter of the presented work was an experimental study of zincand titanium substituted magnetite by means of the nuclear magnetic resonancespectroscopy. The goal was to extend the knowledge about the impact of cationicsubstitutions on the NMR spectra by performing a series of experiments on setsof single crystal samples while focusing on the temperature dependences of thespectra above the Verwey transition. This work shows the particular suitability ofthe NMR method and of the zinc and titanium substitution for the investigationof electronic structure of magnetite. Moreover, the results of this study contributeto the set of information about magnetite that has been systematically collectedby NMR and many other methods for a long period of time.

The temperature dependences of the spectra were measured from the temper-atures near the Verwey transition up to the ambient temperature. In addition,NMR spectra were acquired also below the Verwey transition at the temperatureof 4.2 K. Frequencies of the main spectral lines correspond to those in the spectraof pure magnetite. The broadening of the spectral lines due to the presence of thesubstitution was stated. In case of a high substitution concentration, the spectralose resolution as the lines in the spectra merge together. The structures of satel-lite signals induced by the substitution presence were observed in the spectra ofboth the zinc and the titanium substituted samples acquired above the Verweytransition temperature.

Frequencies of both the main lines and the satellite signals in the spectraabove the Verwey transition were found and their temperature dependences wereconstructed. Satellite lines of particular interest were identified in the spectra ofboth zinc and titanium substituted magnetite and the temperature dependencesof their frequencies were compared to those of the satellites found in the spectraof magnetite with other substitutions and of non-stoichiometric magnetite.

Temperature dependences of the widths of the A lines in the acquired spectraabove the Verwey transition were constructed. These dependences exhibit narrow-ing of the A lines with increasing temperature, which represents a very unusualbehaviour among the magnetically ordered iron oxides. A comparison with thedata for pure magnetite, aluminium substituted magnetite and non-stoichiometricmagnetite was performed and the emphasizing of the effect by the presence of thesubstitution or vacancies was stated.

In the scope of further study, NMR experiments on the investigated samplesshould be performed at higher temperatures in order to track the behaviour of

71

both the main lines and the satellite signals, while taking special care to observethe changes of the width of the A lines and the satellite shifts with increasingtemperature. Detailed information about the origin of the satellite signals in thespectra could be provided by measuring angular dependences of the spectra in anexternal magnetic field. This type of experiment could be also beneficial in theinterpretation of the narrowing of the A lines with increasing temperature. Lastbut not least, employment of ab-initio calculations for further interpretation ofthe experimental results will be considered.

72

Appendix A

Temperature Dependences ofNMR Spectra of Zinc SubstitutedMagnetite Samples

73

67 68 69 70 71 72 73 74 75

I [a.

u.]

f [MHz]

tw = 47 µs115.7 - 115.3 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 47 µs120 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 47 µs124 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 47 µs128.0 - 127.4 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 62 µs144 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 62 µs168 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 62 µs198 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 62 µs216 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 77 µs237.0 - 237.3 K echo 3 - 51

15x echo 3 - 51

I [a.

u.]

tw = 97 µs299 K echo 3 - 101

15x echo 3 - 101

Figure A.1: Temperature dependence of NMR spectra of sample Zn1 in therange 67 – 75 MHz

74

67 67.5 68 68.5 69 69.5 70 70.5 71

I [a.

u.]

f [MHz]

tw = 47 µs115.7 - 115.3 K

I [a.

u.]

tw = 47 µs120 K

I [a.

u.]

tw = 47 µs124 K

I [a.

u.]

tw = 47 µs128.0 - 127.4 K

I [a.

u.]

tw = 62 µs144 K

I [a.

u.]

tw = 62 µs168 K

I [a.

u.]

tw = 62 µs198 K

I [a.

u.]

tw = 62 µs216 K

I [a.

u.]

tw = 77 µs237.0 - 237.3 K

I [a.

u.]

tw = 97 µs299 K

Figure A.2: Temperature dependence of NMR spectra of sample Zn1 in therange 67 – 71 MHz (detail of fig. A.1; see fig. A.1 for key)

75

61 62 63 64 65 66 67 68 69

I [a.

u.]

f [MHz]

tw = 32 µs115.7 K echo 3 - 30

5x echo 3 - 30

I [a.

u.]

tw = 32 µs120 K echo 3 - 30

5x echo 3 - 30

I [a.

u.]

tw = 32 µs124 K echo 3 - 30

5x echo 3 - 30

I [a.

u.]

tw = 32 µs128 K echo 3 - 30

5x echo 3 - 3020x * echo 3 - 51

I [a.

u.]

tw = 32 µs144 K echo 3 - 30

5x echo 3 - 30

I [a.

u.]

tw = 32 µs168 K echo 3 - 30

5x echo 3 - 3020x * echo 3 - 51

I [a.

u.]

tw = 32 µs198 K echo 3 - 30

5x echo 3 - 3020x * echo 3 - 51

I [a.

u.]

tw = 32 µs216 K echo 3 - 30

5x echo 3 - 3020x * echo 3 - 51

I [a.

u.]

tw = 32 µs237 K echo 3 - 30

5x echo 3 - 3020x * echo 3 - 51

I [a.

u.]

tw = 23 µs

299 K echo 3 - 435x echo 3 - 43

20x echo 3 - 81

Figure A.3: Temperature dependence of NMR spectra of sample Zn1 in therange 61 – 69.5 MHz

76

67 68 69 70 71 72 73 74 75

I [a.

u.]

f [MHz]

114.6 K echo 3 - 51 (tw = 257 µs)15x echo 3 - 51 (tw = 257 µs)60x echo 3 - 51 (tw = 57 µs)

I [a.

u.]

tw = 257 µs118.5 K echo 3 - 41

15x echo 3 - 41100x * echo 3 - 12

I [a.

u.] 123.4 K echo 3 - 51 (tw = 257 µs)

15x echo 3 - 51 (tw = 257 µs)150x echo 3 - 51 (tw = 57 µs)

I [a.

u.] 130.5 K echo 3 - 51 (tw = 367 µs)


75x echo 3 - 136 (tw = 102 µs)

I [a.

u.] 144 K echo 3 - 51 (tw = 367 µs)


50x echo 3 - 136 (tw = 102 µs)

I [a.

u.] 167.5 K echo 3 - 51 (tw = 367 µs)


60x echo 3 - 136 (tw = 102 µs)

I [a.

u.]

tw = 263 µs


echo 3 - 91echo 3 - 20

15x echo 3 - 9115x echo 3 - 20

I [a.

u.] 216.6 K echo 3 - 51 (tw = 367 µs)


50x echo 3 - 136 (tw = 102 µs)

I [a.

u.] 240.5 K

sat. 240.5 - 235.0 K


150x * echo 3 - 136 (tw = 102 µs)40x echo 3 - 136 (tw = 102 µs)

I [a.

u.]

tw = 307 µs273 K echo 3 - 17

15x echo 3 - 17

I [a.

u.]

tw = 344 µs

299 K echo 3 - 4115x echo 3 - 41


77

67 67.5 68 68.5 69 69.5 70 70.5 71

I [a.

u.]

f [MHz]

114.6 K

I [a.

u.]

tw = 257 µs118.5 K

I [a.

u.] 123.4 K

I [a.

u.] 130.5 K

I [a.

u.] 144 K

I [a.

u.] 167.5 K

I [a.

u.]

tw = 263 µs


I [a.

u.] 216.6 K

I [a.

u.] 240.5 K

sat. 240.5 - 235.0 K

I [a.

u.]

tw = 307 µs273 K

I [a.

u.]

tw = 344 µs

299 K


78

61 62 63 64 65 66 67 68 69

I [a.

u.]

f [MHz]

tw = 45 µs114.6 K echo 3 - 25

5x echo 3 - 25

I [a.

u.]

tw = 45 µs118.6 K echo 3 - 31

5x echo 3 - 31

I [a.

u.]

tw = 45 µs123.3 K echo 3 - 31

5x echo 3 - 31

I [a.

u.]

tw = 51 µs130.5 K echo 3 - 31

5x echo 3 - 31

I [a.

u.]

tw = 45 µs144 K echo 3 - 31

5x echo 3 - 31

I [a.

u.]

tw = 51 µs167.4 K echo 3 - 31

5x echo 3 - 3120x * echo 3 - 19

I [a.

u.]

tw = 61 µs


echo 3 - 505x echo 3 - 50

I [a.

u.]

tw = 51 µs216.6 K echo 3 - 31

5x echo 3 - 3120x * echo 3 - 31

I [a.

u.]

tw = 51 µs240.5 K echo 3 - 31

5x echo 3 - 3120x * echo 3 - 31

I [a.

u.]

tw = 57 µs273 K echo 3 - 15

5x echo 3 - 15

I [a.

u.]

tw = 62 µs299 K echo 3 - 37

5x echo 3 - 37


79

67 68 69 70 71 72 73 74 75

I [a.

u.]

f [MHz]

tw = 47 µs

106 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

128 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

144 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

168 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

197 - 198 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

216 - 217 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 47 µs

237 K echo 3 - 5140x * echo 3 - 51

I [a.

u.]

tw = 63 µs

273 K echo 3 - 5110x - echo 3 - 51

I [a.

u.]

tw = 344 µs

299 K echo 3 - 3140x * echo 3 - 31


80

67 67.5 68 68.5 69 69.5 70 70.5 71

I [a.

u.]

f [MHz]

tw = 47 µs

106 K

I [a.

u.]

tw = 47 µs

128 K

I [a.

u.]

tw = 47 µs

144 K

I [a.

u.]

tw = 47 µs

168 K

I [a.

u.]

tw = 47 µs

197 - 198 K

I [a.

u.]

tw = 47 µs

216 - 217 K

I [a.

u.]

tw = 47 µs

237 K

I [a.

u.]

tw = 63 µs

273 K

I [a.

u.]

tw = 344 µs

299 K


81

61 62 63 64 65 66 67 68 69

I [a.

u.]

f [MHz]

tw = 32 µs

106 K echo 3 - 12

I [a.

u.]

tw = 32 µs

128 K echo 3 - 30

I [a.

u.]

tw = 32 µs

144 K echo 3 - 30

I [a.

u.]

tw = 32 µs

168 K echo 3 - 305x * echo 3 - 51

I [a.

u.]

tw = 32 µs

197.5 K echo 3 - 30

I [a.

u.]

tw = 32 µs

216 K echo 3 - 305x * echo 3 - 51

I [a.

u.]

tw = 32 µs

237.3 K echo 3 - 305x * echo 3 - 51

I [a.

u.]

tw = 21 µs

273 K echo 3 - 51

I [a.

u.]

tw = 47 µs

299 K echo 3 - 41


82

Appendix B

Temperature Dependences ofSpectral Signal Frequencies ofZinc Substituted MagnetiteSamples - Tables

83

Table

B.1

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Zn1

-par

t1

B

Strá

nka

1

B11

5.7

66.4

0 ±

0.04

67.8

4 ±

0.06

120.

066

.35

± 0.

0467

.64

± 0.

1012

4.0

66.3

2 ±

0.10

128.

063

.85

± 0.

3565

.540

± 0

.030

66.4

00 ±

0.0

3014

4.0

63.8

2 ±

0.15

65.2

40 ±

0.0

2066

.235

± 0

.015

66.7

70 ±

0.0

5016

8.0

63.6

8 ±

0.15

64.8

55 ±

0.0

1565

.130

± 0

.020

65.3

20 ±

0.0

3065

.955

± 0

.015

66.4

10 ±

0.0

3068

.30

± 0.

3019

8.0

63.3

6 ±

0.08

64.3

20 ±

0.0

3064

.415

± 0

.015

64.8

00 ±

0.0

3065

.525

± 0

.010

65.8

80 ±

0.0

3067

.94

± 0.

1221

6.0

63.1

3 ±

0.10

64.0

30 ±

0.0

2564

.142

± 0

.010

64.4

10 ±

0.0

3064

.650

± 0

.020

65.2

28 ±

0.0

1065

.540

± 0

.030

67.4

6 ±

0.15

237.

062

.86

± 0.

0663

.726

± 0

.020

63.8

14 ±

0.0

1064

.110

± 0

.025

64.8

60 ±

0.0

1065

.140

± 0

.025

299.

061

.63

± 0.

0462

.485

± 0

.015

62.5

57 ±

0.0

0762

.770

± 0

.050

63.4

46 ±

0.0

0563

.644

± 0

.025

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

sat 1

sat 2

B 1sa

t 3sa

t 4B 2

sat 5

sat 6

sat 7

84

Table

B.2

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Zn1

-par

t2

A

Strá

nka

1

A11

5.5

69.4

40 ±

0.0

0569

.468

± 0

.007

69.6

52 ±

0.0

0369

.806

± 0

.005

69.8

44 ±

0.0

0570

.760

± 0

.060

120.

069

.417

± 0

.005

69.4

44 ±

0.0

0569

.623

± 0

.003

69.7

73 ±

0.0

0569

.814

± 0

.005

70.6

50 ±

0.0

9012

4.0

69.3

90 ±

0.0

0569

.413

± 0

.005

69.5

93 ±

0.0

0369

.735

± 0

.010

127.

769

.355

± 0

.007

69.3

95 ±

0.0

0569

.561

± 0

.002

69.6

99 ±

0.0

0614

4.0

69.2

44 ±

0.0

0569

.281

± 0

.003

69.4

33 ±

0.0

0269

.558

± 0

.005

168.

069

.077

± 0

.004

69.1

05 ±

0.0

0369

.183

± 0

.004

69.2

42 ±

0.0

0369

.330

± 0

.015

69.4

03 ±

0.0

1569

.524

± 0

.010

198.

068

.830

± 0

.003

68.8

57 ±

0.0

0368

.933

± 0

.003

68.9

78 ±

0.0

0369

.048

± 0

.005

69.1

19 ±

0.0

0569

.250

± 0

.010

216.

068

.661

± 0

.003

68.6

81 ±

0.0

0368

.755

± 0

.004

68.8

00 ±

0.0

0368

.857

± 0

.004

68.9

20 ±

0.0

1023

7.2

68.4

45 ±

0.0

0368

.465

± 0

.003

68.5

31 ±

0.0

0468

.576

± 0

.002

68.6

20 ±

0.0

0568

.688

± 0

.005

68.8

38 ±

0.0

0629

9.0

67.5

72 ±

0.0

0367

.588

± 0

.003

67.6

36 ±

0.0

0767

.680

± 0

.002

67.7

39 ±

0.0

0567

.761

± 0

.004

67.8

90 ±

0.0

10

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

sat 8

sat 9

sat 1

0sa

t 15

sat 1

6sa

t 18

sat 2

0

85

Table

B.3

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Zn2

-par

t1

B

Strá

nka

1

B11

4.6

66.3

90 ±

0.0

5067

.78

± 0.

1011

8.6

66.3

54 ±

0.0

3067

.70

± 0.

1012

3.3

66.3

00 ±

0.0

2067

.58

± 0.

1013

0.5

65.4

72 ±

0.0

1566

.405

± 0

.015

144.

065

.227

± 0

.010

66.2

48 ±

0.0

1066

.800

± 0

.050

167.

463

.75

± 0.

1064

.863

± 0

.006

65.3

15 ±

0.0

1565

.967

± 0

.006

66.4

25 ±

0.0

4019

8.0

64.3

40 ±

0.0

5064

.451

± 0

.010

65.5

71 ±

0.0

0865

.920

± 0

.050

216.

663

.14

± 0.

0864

.115

± 0

.005

64.4

30 ±

0.0

5065

.211

± 0

.005

65.5

30 ±

0.0

4024

0.5

62.8

0 ±

0.05

63.6

06 ±

0.0

1563

.717

± 0

.006

64.0

19 ±

0.0

1564

.762

± 0

.006

65.0

25 ±

0.0

3027

3.0

62.1

7 ±

0.06

63.0

20 ±

0.0

1063

.118

± 0

.006

63.3

90 ±

0.0

5064

.086

± 0

.005

64.3

06 ±

0.0

2029

9.0

61.6

4 ±

0.04

62.4

83 ±

0.0

0862

.578

± 0

.004

62.8

05 ±

0.0

5063

.492

± 0

.004

63.6

85 ±

0.0

10

Temperature

Frequency f [

MH

z]T

[K] ±

0.5

sat 1

sat 2

B1

sat 3

sat 4

B2

sat 5

sat 6

86

Table

B.4

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Zn2

-par

t2

(sat

ellite

sm

arke

dby

anas

teri

sk(”

*”)

aris

efr

omth

epre

sence

ofva

canci

es–

see

the

text)

A

Strá

nka

1

A11

4.6

69.4

40 ±

0.0

0569

.465

± 0

.005

69.6

54 ±

0.0

0469

.800

± 0

.005

118.

569

.418

± 0

.003

69.4

48 ±

0.0

0469

.627

± 0

.002

69.7

80 ±

0.0

0512

3.4

69.3

87 ±

0.0

0369

.418

± 0

.003

69.5

38 ±

0.0

0369

.588

± 0

.002

69.6

13 ±

0.0

0369

.649

± 0

.002

69.7

37 ±

0.0

0313

0.5

69.3

35 ±

0.0

0769

.372

± 0

.007

69.5

25 ±

0.0

0369

.534

± 0

.001

69.5

52 ±

0.0

0369

.563

± 0

.002

69.6

75 ±

0.0

1514

4.0

69.2

37 ±

0.0

0369

.277

± 0

.003

69.3

70 ±

0.0

0269

.418

± 0

.002

69.4

273

± 0.

0010

69.4

41 ±

0.0

0269

.483

± 0

.002

69.5

07 ±

0.0

0369

.556

± 0

.010

69.5

90 ±

0.0

0516

7.5

69.0

73 ±

0.0

0369

.104

± 0

.003

69.1

86 ±

0.0

0269

.241

5 ±

0.00

1069

.257

± 0

.002

69.2

86 ±

0.0

0269

.345

± 0

.005

69.3

89 ±

0.0

0519

8.0

68.8

78 ±

0.0

0568

.946

± 0

.005

68.9

69 ±

0.0

0368

.997

± 0

.003

69.0

08 ±

0.0

0469

.028

± 0

.004

69.0

68 ±

0.0

0721

6.6

68.6

50 ±

0.0

0368

.671

± 0

.003

68.7

39 ±

0.0

0268

.787

6 ±

0.00

1068

.846

± 0

.003

68.9

12 ±

0.0

0524

0.5

68.3

86 ±

0.0

0368

.406

± 0

.002

68.4

70 ±

0.0

0368

.514

7 ±

0.00

0568

.554

± 0

.003

68.6

23 ±

0.0

0527

3.0

67.9

64 ±

0.0

0568

.032

± 0

.001

68.0

753

± 0.

0003

68.1

60 ±

0.0

1029

9.0

67.5

82 ±

0.0

0267

.594

± 0

.003

67.6

40 ±

0.0

0267

.650

± 0

.003

67.6

919

± 0.

0003

67.7

45 ±

0.0

0567

.772

± 0

.005

114.

670

.720

± 0

.050

72.2

20 ±

0.0

5072

.630

± 0

.050

118.

569

.820

± 0

.010

70.1

10 ±

0.0

6070

.680

± 0

.060

72.1

60 ±

0.1

0072

.620

± 0

.040

123.

469

.786

± 0

.010

72.5

60 ±

0.0

3013

0.5

70.1

10 ±

0.0

4014

4.0

69.6

30 ±

0.0

0669

.693

± 0

.010

69.9

90 ±

0.0

2571

.220

± 0

.030

72.1

70 ±

0.0

8073

.010

± 0

.040

167.

569

.417

± 0

.005

69.7

70 ±

0.0

3070

.940

± 0

.040

71.7

80 ±

0.0

3072

.660

± 0

.030

198.

021

6.6

68.9

85 ±

0.0

0769

.045

± 0

.005

69.2

25 ±

0.0

1524

0.5

68.7

04 ±

0.0

1068

.762

± 0

.005

68.9

20 ±

0.0

1027

3.0

299.

0

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

sat 8

sat 9

sat 1

0sa

t 11

sat 1

2sa

t 13

sat 1

4sa

t 15

sat 1

6

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

sat 1

7sa

t 18

sat 1

9 *

sat 2

0sa

t 21

*sa

t 22

*sa

t 23

*sa

t 24

*sa

t 25

*

87

Table

B.5

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Zn3

-par

t1

B

Strá

nka

1

B10

6.0

66.5

03 ±

0.0

7512

8.0

65.6

00 ±

0.0

7566

.340

± 0

.075

144.

065

.320

± 0

.060

66.2

30 ±

0.0

5016

8.0

63.5

6 ±

0.10

64.8

60 ±

0.0

5065

.928

± 0

.040

197.

564

.400

± 0

.060

64.7

20 ±

0.0

6065

.510

± 0

.040

216.

063

.10

± 0.

2064

.136

± 0

.040

64.4

20 ±

0.0

7565

.200

± 0

.040

65.5

70 ±

0.0

5023

7.3

62.8

0 ±

0.06

63.7

70 ±

0.0

4064

.070

± 0

.060

64.8

20 ±

0.0

4065

.100

± 0

.050

273.

062

.18

± 0.

0663

.090

± 0

.020

63.3

50 ±

0.0

4063

.600

± 0

.050

64.0

50 ±

0.0

2064

.280

± 0

.040

299.

061

.58

± 0.

1062

.564

± 0

.015

62.8

40 ±

0.0

6063

.485

± 0

.010

63.6

70 ±

0.0

25

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

sat 1

B 1sa

t 3sa

t 4B

2sa

t 5

88

Table

B.6

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Zn3

-par

t2

A

Strá

nka

1

A10

6.0

69.5

15 ±

0.0

1069

.728

± 0

.003

71.0

6 ±

0.10

128.

069

.370

± 0

.020

69.5

64 ±

0.0

0469

.717

± 0

.050

144.

069

.260

± 0

.030

69.4

42 ±

0.0

0469

.570

± 0

.030

168.

069

.110

± 0

.010

69.2

47 ±

0.0

0469

.344

± 0

.020

69.5

20 ±

0.0

2019

7.5

67.9

4 ±

0.15

68.8

58 ±

0.0

2068

.937

± 0

.010

68.9

88 ±

0.0

0569

.060

± 0

.007

69.1

28 ±

0.0

0769

.263

± 0

.007

216.

567

.43

± 0.

0868

.666

± 0

.010

68.7

52 ±

0.0

0768

.796

± 0

.005

68.8

53 ±

0.0

0768

.916

± 0

.007

69.0

80 ±

0.0

1523

7.0

68.4

45 ±

0.0

0768

.517

± 0

.007

68.5

60 ±

0.0

0468

.602

± 0

.007

68.6

72 ±

0.0

0727

3.0

67.9

54 ±

0.0

0868

.024

± 0

.004

68.0

66 ±

0.0

0268

.154

± 0

.006

299.

067

.583

± 0

.005

67.6

41 ±

0.0

0467

.687

± 0

.002

67.7

50 ±

0.0

15

Temperature

Frequency f [

MH

z]T

[K] ±

0.5

sat 7

sat 9

sat 1

0sa

t 15

sat 1

6sa

t 18

sat 2

0

89

Appendix C

Temperature Dependences ofHWHM of the A Lines of ZincSubstituted Magnetite Samples -Tables

Table C.1: Temperature dependence of half width at half maximum of the Aline of the sample Zn1

Temperature T [K] ±0.5 A HWHM [kHz] ±0.20115.5 32.95120.0 31.15124.0 28.80127.7 27.30144.0 21.90168.0 16.50198.0 12.20216.0 10.80237.2 9.25299.0 7.70

90


Temperature T [K] ±0.5 A HWHM [kHz] ±0.20114.6 32.50118.5 18.00123.4 4.50130.5 3.50144.0 3.50167.5 2.95198.0 2.65216.6 2.50240.5 2.65273.0 2.40299.0 2.65


Temperature T [K] ±0.5 A HWHM [kHz] ±0.20106.0 87.90128.0 53.85144.0 42.35168.0 30.95197.5 22.35216.5 18.35237.0 16.15273.0 13.80299.0 12.75

91

Appendix D

Temperature Dependences ofNMR Spectra of TitaniumSubstituted Magnetite Samples

92

66 67 68 69 70 71 72 73 74

I [a.

u.]

f [MHz]

tw = 47 µs114 K echo 3 - 126

echo 3 - 501

I [a.

u.]

tw = 47 µs116 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs116.5 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs119 - 117 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs124 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs128 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs136 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 47 µs144 K echo 3 - 201

echo 3 - 5130x * echo 3 - 201

I [a.

u.]

tw = 67 µs168 K echo 3 - 134

echo 3 - 3430x * echo 3 - 134

I [a.

u.]

tw = 67 µs198 K echo 3 - 134

echo 3 - 3430x * echo 3 - 134

I [a.

u.]

tw = 67 µs216 - 215.4 K echo 3 - 134

echo 3 - 3430x * echo 3 - 134

I [a.

u.]

tw = 97 µs237 K echo 3 - 91

echo 3 - 2330x * echo 3 - 91

I [a.

u.]

tw = 77 µs273 K echo 3 - 51

echo 3 - 2930x * echo 3 - 51

I [a.

u.]

tw = 97 µs299 K echo 3 - 91

echo 3 - 2330x echo 3 - 91

30x satellites - echo 3 - 151

Figure D.1: Temperature dependence of NMR spectra of sample Ti1 in the range65.5 – 74.5 MHz

93

67 67.5 68 68.5 69 69.5 70 70.5 71

I [a.

u.]

f [MHz]

tw = 47 µs114 K

I [a.

u.]

tw = 47 µs116 K

I [a.

u.]

tw = 47 µs116.5 K

I [a.

u.]

tw = 47 µs119 - 117 K

I [a.

u.]

tw = 47 µs124 K

I [a.

u.]

tw = 47 µs128 K

I [a.

u.]

tw = 47 µs136 K

I [a.

u.]

tw = 47 µs144 K

I [a.

u.]

tw = 67 µs168 K

I [a.

u.]

tw = 67 µs198 K

I [a.

u.]

tw = 67 µs216 - 215.4 K

I [a.

u.]

tw = 97 µs237 K

I [a.

u.]

tw = 77 µs273 K

I [a.

u.]

tw = 97 µs299 K

Figure D.2: Temperature dependence of NMR spectra of sample Ti1 in the range67 – 71 MHz (detail of fig. D.1; see fig. D.1 for key)

94

61 62 63 64 65 66 67 68 69

I [a.

u.]

f [MHz]

114 K

I [a.

u.]

tw = 19 µs116 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs116.5 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs118 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs124 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs128 K echo 3 - 36

echo 3 - 12

I [a.

u.]

tw = 19 µs136 K echo 3 - 36

echo 3 - 125x echo 3 - 36

I [a.

u.]

tw = 19 µs144 K echo 3 - 36

echo 3 - 125x echo 3 - 36

I [a.

u.]

tw = 19 µs168 K echo 3 - 81

echo 3 - 36echo 3 - 12

5x echo 3 - 81

I [a.

u.]

tw = 19 µs198 K echo 3 - 81

echo 3 - 36echo 3 - 12

5x echo 3 - 81

I [a.

u.]

tw = 19 µs216 K echo 3 - 81

echo 3 - 36echo 3 - 12

5x echo 3 - 81

I [a.

u.]

tw = 23 µs237 K echo 3 - 81

echo 3 - 66echo 3 - 30

echo 3 - 105x echo 3 - 81

I [a.

u.]

tw = 77 µs273 K echo 3 - 24

echo 3 - 20echo 3 - 9

5x echo 3 - 24

I [a.

u.]

tw = 23 µs299 K echo 3 - 81

echo 3 - 66echo 3 - 30

echo 3 - 105x echo 3 - 81

Figure D.3: Temperature dependence of NMR spectra of sample Ti1 in the range61 – 69.5 MHz

95

66 67 68 69 70 71 72 73 74

I [a.

u.]

f [MHz]

tw = 47 µs

109 K echo 3 - 301echo 3 - 51

I [a.

u.]

tw = 47 µs

115.7 - 116.6 K echo 3 - 301echo 3 - 51

100x echo 3 - 301

I [a.

u.]

tw = 47 µs

124.0 - 123.5 K echo 3 - 301echo 3 - 51

100x echo 3 - 301

I [a.

u.]

tw = 47 µs

128.0 - 127.3 K echo 3 - 301echo 3 - 51

100x echo 3 - 301

I [a.

u.]

tw = 67 µs

144 K echo 3 - 301echo 3 - 36

100x echo 3 - 201

I [a.

u.]

tw = 67 µs

168 K echo 3 - 301echo 3 - 36

100x echo 3 - 201

I [a.

u.]

tw = 67 µs

198 K echo 3 - 301echo 3 - 36

100x echo 3 - 201

I [a.

u.] 236.3 - 237.0 K echo 3 - 151 (tw = 97 µs)


100x * echo 3 - 301 (tw = 47 µs)

I [a.

u.]

tw = 97 µs

298 K echo 3 - 151echo 3 - 26

100x echo 3 - 151100x * echo 3 - 100


96

67 67.5 68 68.5 69 69.5 70 70.5 71

I [a.

u.]

f [MHz]

tw = 47 µs

109 K

I [a.

u.]

tw = 47 µs

115.7 - 116.6 K

I [a.

u.]

tw = 47 µs

124.0 - 123.5 K

I [a.

u.]

tw = 47 µs

128.0 - 127.3 K

I [a.

u.]

tw = 67 µs

144 K

I [a.

u.]

tw = 67 µs

168 K

I [a.

u.]

tw = 67 µs

198 K

I [a.

u.] 236.3 - 237.0 K

I [a.

u.]

tw = 97 µs

298 K


97

61 62 63 64 65 66 67 68 69

I [a.

u.]

f [MHz]

109 K

I [a.

u.]

tw = 19 µs

116 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

124 K echo 3 - 51echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

128 K echo 3 - 51echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

144 K echo 3 - 81echo 3 - 51echo 3 - 36

echo 3 - 1210x echo 3 - 81

I [a.

u.]

tw = 19 µs

168 K echo 3 - 81echo 3 - 51echo 3 - 36

echo 3 - 1210x echo 3 - 81

I [a.

u.]

tw = 19 µs

198.0 - 198.4 K

echo 3 - 81echo 3 - 51echo 3 - 36

echo 3 - 1210x echo 3 - 81

I [a.

u.]

tw = 23 µs

236.7 - 236.4 K echo 3 - 81echo 3 - 66echo 3 - 30

echo 3 - 1010x echo 3 - 81

I [a.

u.]

tw = 23 µs

298.7 - 299.5 K echo 3 - 81echo 3 - 66echo 3 - 30

echo 3 - 1010x echo 3 - 81


98

66 67 68 69 70 71 72 73 74

I [a.

u.]

f [MHz]

tw = 47 µs

95 K echo 3 - 201echo 3 - 51

15x echo 3 - 201

I [a.

u.]

tw = 47 µs

109.0 - 108.2 K echo 3 - 201echo 3 - 51

15x echo 3 - 201

I [a.

u.]

tw = 47 µs

124.0 - 122.3 K echo 3 - 201echo 3 - 51

15x echo 3 - 201

I [a.

u.]

tw = 47 µs

128.0 - 128.5 K echo 3 - 201echo 3 - 51

15x echo 3 - 201

I [a.

u.]

tw = 67 µs

144 K echo 3 - 134echo 3 - 34

15x echo 3 - 134

I [a.

u.]

tw = 67 µs

198 K echo 3 - 134echo 3 - 34

15x echo 3 - 134

I [a.

u.]

tw = 97 µs

237 K echo 3 - 91echo 3 - 23

15x echo 3 - 91

I [a.

u.]

tw = 97 µs

299 K echo 3 - 91echo 3 - 23

15x echo 3 - 91


99

67 67.5 68 68.5 69 69.5 70 70.5 71

I [a.

u.]

f [MHz]

tw = 47 µs

95 K

I [a.

u.]

tw = 47 µs

109.0 - 108.2 K

I [a.

u.]

tw = 47 µs

124.0 - 122.3 K

I [a.

u.]

tw = 47 µs

128.0 - 128.5 K

I [a.

u.]

tw = 67 µs

144 K

I [a.

u.]

tw = 67 µs

198 K

I [a.

u.]

tw = 97 µs

237 K

I [a.

u.]

tw = 97 µs

299 K


100

61 62 63 64 65 66 67 68 69

I [a.

u.]

f [MHz]

tw = 19 µs

95.0 - 95.6 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

109 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

124 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

128 K echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

144 K echo 3 - 81echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 19 µs

198 K echo 3 - 81echo 3 - 36echo 3 - 12

I [a.

u.]

tw = 97 µs

237 K echo 3 - 81echo 3 - 66echo 3 - 30echo 3 - 10

I [a.

u.]

tw = 97 µs

299.4 K echo 3 - 81echo 3 - 66echo 3 - 30echo 3 - 10


101

Appendix E

Temperature Dependences ofSpectral Signal Frequencies ofTitanium Substituted MagnetiteSamples - Tables

102

Table

E.1

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Ti1

-par

t1

B

Strá

nka

1

B11

6.0

66.3

30 ±

0.0

6011

6.5

66.3

50 ±

0.0

2511

8.0

66.3

70 ±

0.0

3012

4.0

66.3

00 ±

0.0

3512

8.0

65.7

5 ±

0.15

66.4

30 ±

0.0

6013

6.0

65.3

90 ±

0.0

3066

.350

± 0

.020

144.

065

.250

± 0

.030

66.2

70 ±

0.0

3016

8.0

64.8

70 ±

0.0

3065

.970

± 0

.025

66.5

70 ±

0.0

6019

8.0

64.4

28 ±

0.0

2065

.000

± 0

.040

65.5

45 ±

0.0

1566

.060

± 0

.060

216.

064

.150

± 0

.015

64.7

00 ±

0.0

7065

.250

± 0

.010

65.7

70 ±

0.0

4023

7.0

63.8

00 ±

0.0

1064

.300

± 0

.050

64.8

60 ±

0.0

1065

.320

± 0

.050

273.

063

.091

± 0

.007

63.5

10 ±

0.0

4064

.066

± 0

.004

64.4

80 ±

0.0

4029

9.0

62.5

80 ±

0.0

0662

.960

± 0

.040

63.4

75 ±

0.0

0363

.860

± 0

.030

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

B1

sat 2

B2

sat 4

103

Table

E.2

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Ti1

-par

t2

A

Strá

nka

1

A11

6.0

68.3

40 ±

0.0

6068

.630

± 0

.030

69.3

80 ±

0.0

4069

.643

± 0

.006

116.

568

.320

± 0

.030

68.6

10 ±

0.0

2069

.400

± 0

.015

69.6

38 ±

0.0

0370

.145

± 0

.010

68.3

00 ±

0.0

2068

.600

± 0

.015

69.3

90 ±

0.0

1069

.627

± 0

.003

70.1

30 ±

0.0

0712

4.0

68.2

80 ±

0.0

1568

.560

± 0

.020

69.3

60 ±

0.0

1569

.588

± 0

.003

70.0

85 ±

0.0

1512

8.0

68.3

80 ±

0.0

2069

.378

± 0

.015

69.4

85 ±

0.0

1569

.558

± 0

.004

70.1

10 ±

0.0

1513

6.0

68.2

74 ±

0.0

1568

.480

± 0

.020

69.3

10 ±

0.0

1069

.495

± 0

.005

69.8

13 ±

0.0

0770

.010

± 0

.010

144.

068

.210

± 0

.010

68.4

17 ±

0.0

1069

.248

± 0

.010

69.4

34 ±

0.0

0569

.735

± 0

.015

69.9

27 ±

0.0

1016

8.0

68.0

00 ±

0.0

2068

.203

± 0

.010

69.0

66 ±

0.0

1069

.243

± 0

.003

69.2

95 ±

0.0

0869

.486

± 0

.007

69.6

85 ±

0.0

1019

8.0

67.6

55 ±

0.0

1067

.692

± 0

.010

67.8

77 ±

0.0

0768

.805

± 0

.010

68.9

42 ±

0.0

1068

.981

± 0

.003

69.3

52 ±

0.0

1021

5.7

67.4

35 ±

0.0

0667

.462

± 0

.006

67.6

45 ±

0.0

0668

.630

± 0

.007

68.7

20 ±

0.0

1568

.804

± 0

.005

68.8

39 ±

0.0

0569

.139

± 0

.010

237.

067

.120

± 0

.010

67.1

62 ±

0.0

1067

.330

± 0

.010

68.3

95 ±

0.0

0868

.493

± 0

.015

68.5

68 ±

0.0

0268

.596

± 0

.007

68.8

60 ±

0.0

1027

3.0

66.4

23 ±

0.0

0766

.480

± 0

.007

66.6

35 ±

0.0

0767

.886

± 0

.003

67.9

94 ±

0.0

1068

.040

± 0

.003

68.0

712

± 0.

0015

68.1

03 ±

0.0

0268

.295

± 0

.010

299.

065

.939

± 0

.010

66.0

07 ±

0.0

0766

.142

± 0

.007

67.4

88 ±

0.0

0567

.590

± 0

.010

67.6

790

± 0.

0015

67.7

04 ±

0.0

07

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

sat 5

sat 6

sat 7

sat 8

sat 9

sat 1

0sa

t 11

sat 1

2sa

t 13

118.

0 ±

1.0

104

Table

E.3

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Ti2

-par

t1

B

Strá

nka

1

B11

6.0

66.4

00 ±

0.0

2512

4.0

66.3

00 ±

0.0

1512

8.0

65.9

0 ±

0.10

66.5

00 ±

0.0

1014

4.0

65.2

30 ±

0.0

1066

.246

± 0

.007

168.

064

.826

± 0

.005

65.9

50 ±

0.0

0519

8.2

64.3

84 ±

0.0

0464

.480

± 0

.015

64.9

60 ±

0.0

5065

.508

± 0

.003

65.6

10 ±

0.0

1565

.990

± 0

.040

236.

663

.753

± 0

.003

63.8

38 ±

0.0

1064

.260

± 0

.035

64.8

26 ±

0.0

0364

.900

± 0

.020

65.3

00 ±

0.0

5029

9.1

62.3

30 ±

0.0

0362

.400

± 0

.010

62.6

90 ±

0.0

4063

.196

± 0

.003

63.2

70 ±

0.0

1063

.580

± 0

.050

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

B1

sat 1

sat 2

B2

sat 3

sat 4

105

Table

E.4

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Ti2

-par

t2

A

Strá

nka

1

A11

6.2

68.3

20 ±

0.0

2568

.610

± 0

.015

69.6

42 ±

0.0

0212

3.8

68.2

70 ±

0.0

0568

.550

± 0

.010

69.5

845

± 0.

0015

70.0

70 ±

0.0

2012

7.7

68.3

70 ±

0.0

2068

.680

± 0

.040

69.5

540

± 0.

0015

70.1

05 ±

0.0

0714

4.0

68.2

10 ±

0.0

1568

.416

± 0

.010

69.2

44 ±

0.0

0569

.432

± 0

.001

69.9

29 ±

0.0

0516

8.0

67.9

90 ±

0.0

1068

.190

± 0

.010

69.0

65 ±

0.0

0369

.238

± 0

.001

69.6

77 ±

0.0

0719

8.0

67.6

52 ±

0.0

0867

.686

± 0

.007

67.8

75 ±

0.0

0868

.803

± 0

.003

68.9

75 ±

0.0

0169

.370

± 0

.020

236.

767

.095

± 0

.005

67.1

30 ±

0.0

0567

.310

± 0

.005

68.3

93 ±

0.0

0468

.570

± 0

.001

68.8

70 ±

0.0

1029

8.0

65.9

20 ±

0.0

0765

.988

± 0

.005

66.1

21 ±

0.0

0467

.470

± 0

.002

67.6

62 ±

0.0

0167

.831

± 0

.002

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

sat 5

sat 6

sat 7

sat 8

sat 1

3

106

Table

E.5

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Ti3

-par

t1

B

Strá

nka

1

B95

.367

.00

± 0.

4010

9.0

66.6

5 ±

0.20

124.

065

.70

± 0.

2066

.33

± 0.

1512

8.0

65.6

5 ±

0.15

66.3

9 ±

0.10

144.

065

.30

± 0.

1066

.230

± 0

.050

198.

064

.390

± 0

.050

65.4

80 ±

0.0

2565

.960

± 0

.060

237.

063

.780

± 0

.050

64.2

80 ±

0.0

7064

.770

± 0

.025

65.2

40 ±

0.0

6029

9.4

62.4

80 ±

0.0

3062

.820

± 0

.050

63.3

20 ±

0.0

1563

.660

± 0

.040

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

B1

sat 2

B2

sat 4

107

Table

E.6

:T

emp

erat

ure

dep

enden

ces

ofsp

ectr

alsi

gnal

freq

uen

cies

ofth

esa

mple

Ti3

-par

t2

A

Strá

nka

1

A95

.068

.360

± 0

.040

68.6

80 ±

0.0

2569

.727

± 0

.007

70.2

60 ±

0.0

1010

8.6

68.3

50 ±

0.0

2568

.645

± 0

.040

69.6

94 ±

0.0

0670

.210

± 0

.020

68.4

30 ±

0.0

5069

.592

± 0

.006

70.1

25 ±

0.0

2512

8.3

68.3

70 ±

0.0

4068

.510

± 0

.050

69.5

58 ±

0.0

0770

.080

± 0

.015

144.

068

.210

± 0

.040

68.3

60 ±

0.0

4069

.426

± 0

.005

69.9

20 ±

0.0

2019

8.0

67.6

70 ±

0.0

4067

.860

± 0

.030

68.7

98 ±

0.0

0468

.966

± 0

.003

69.3

38 ±

0.0

2023

7.0

67.1

10 ±

0.0

4067

.310

± 0

.025

68.3

70 ±

0.0

0568

.555

± 0

.003

68.8

40 ±

0.0

1529

9.0

65.8

10 ±

0.0

4066

.000

± 0

.020

67.4

15 ±

0.0

0667

.612

± 0

.002

67.7

77 ±

0.0

15

Tem

pera

ture

Freq

uenc

y f [

MH

z]T

[K] ±

0.5

sat 6

sat 7

sat 8

sat 1

3

123.

2 ±

1.0

108

Appendix F

Temperature Dependences ofHWHM of the A Lines ofTitanium Substituted MagnetiteSamples - Tables

Table F.1: Temperature dependence of half width at half maximum of the A lineof the sample Ti1

Temperature T [K] ±0.5 A HWHM [kHz] ±0.20116.0 26.55116.5 25.55

118.0± 1.0 25.50124.0 23.70128.0 22.75136.0 19.60144.0 17.50168.0 12.10198.0 9.30215.7 8.70237.0 7.35273.0 7.30299.0 6.70

109


Temperature T [K] ±0.5 A HWHM [kHz] ±0.20116.2 29.20123.8 17.60127.7 17.40144.0 12.45168.0 9.75198.0 8.60236.7 6.50298.0 6.30


Temperature T [K] ±0.5 A HWHM [kHz] ±0.2095.0 128.30108.6 110.30

123.2± 1.0 99.75128.3 92.10144.0 74.85198.0 44.75237.0 34.15299.0 26.80

110

Bibliography

[1] Mizoguchi M. (2001): Charge and Orbital Ordering Structure of Fe3O4 in theLow-Temperature Phase as Deduced from NMR Study, J. Phys. Soc. Jpn. 70,2333–2344.

[2] Novak P., Stepankova H., Englich J., Kohout J., Brabers V. A. M. (2000):NMR in magnetite below and around the Verwey transition, Phys. Rev. B 61,1256–1260.

[3] Gamaliy E., Stepankova H., Englich J., Kohout J., Snezhko A., Novak P.,Brabers V.A.M. (2002): NMR of 57Fe above the Verwey transition in Al-substituted magnetite, J. Magn. Magn. Mater. 242–245, 732–734.

[4] Kohout J., Gamaliy E., Stepankova H., Englich J., Novak P., Brabers V.A.M.(2004): NMR of 57Fe below and around the Verwey transition in Al-substitutedmagnetite, J. Magn. Magn. Mater. 272–276, e1687–e1688.

[5] Kohout J., Gamaliy E., Stepankova H., Englich J., Prochazka V., ChlanV., Brabers V.A.M. (2005): NMR of 57Fe, 69Ga and 71Ga in Ga substitutedmagnetite, J. Magn. Magn. Mater. 290–291, 1018–1020.

[6] Chlan V., Gamaliy E., Stepankova H., Kouril K., Englich J., Kohout J.,Brabers V. (2007): Nuclear magnetic resonance of 57Fe in Al-, Ga- and Ti-substituted magnetite above Verwey temperature, J. Magn. Magn. Mater. 310,2555–2557.

[7] Reznıcek R.: Spektra jaderne magneticke rezonance magnetitu se substitucızinku, bachelor thesis, MFF UK, Prague, 2008.

[8] Sedlak B., Kuz’min R. N.: Jaderne resonancnı metody ve fyzice pevnych latek,Statnı pedagogicke nakladatelstvı, Praha, 1978.

[9] Meiboom S., Gill D. (1958): Modified Spin-Echo Method for Measuring Nu-clear Relaxation Times, Rev. Sci. Instrum. 29, 688–691.

[10] Walz F. (2002): The Verwey transition–a topical review, J. Phys.: Condens.Matter 14, R285–R340.

[11] Garcıa J., Subıas G. (2004): The Verwey transition–a new perspective, J.Phys.: Condens. Matter 16, R145–R178.

[12] Brabers V. A. M.: Progress in spinel ferrite research. Handbook of MagneticMaterials, ed. K. H. J. Buschow, Elsevier, Amsterdam, 1995.

111

[13] Kakol Z.: Effect of Titanium and Zinc Doping and Influence of StoichiometryChanges on Physical Properties of Magnetite, AGH University, Faculty ofPhysics and Nuclear Techniques, Krakow, 1994.

[14] Krupicka S.: Fyzika feritu a prıbuznych magnetickych kyslicnıku, Academia,Praha, 1969.

[15] Aroyo M. I., Perez-Mato J. M., Capillas C., Kroumova E., Ivantchev S.,Madariaga G., Kirov A., Wondratschek H. (2006): Bilbao CrystallographicServer: I. Databases and crystallographic computing programs, Zeitschrift furKristallographie 221, 1, 15–27.

[16] Iizumi M., Koetzle T. F., Shirane G., Chikazumi S., Matsui M., Todo S.(1982): Structure of magnetite (Fe3O4) below the Verwey transition tempera-ture, Acta Cryst. B 38, 2121–2133.

[17] Wright J. P., Attfield J. P., Radaelli P. G. (2002): Charge ordered structureof magnetite Fe3O4 below the Verwey transition, Phys. Rev. B 66, 214422.

[18] De Grave E., Persoons R. M., Vandenberghe R. E., de Bakker P. M. A. (1993):Mossbauer study of the high-temperature phase of Co-substituted magnetites,CoxFe3−xO4. I. x≤0.04, Phys. Rev. B 47, 5881—5893.

[19] Loos J., Novak P. (2002): Double exchange and superexchange in a ferrimag-netic half-metal, Phys. Rev. B 66, 132403.

[20] Kubo K., Ohata N. (1972): A Quantum Theory of Double Exchange. I, J.Phys. Soc. Jpn. 33, 21.

[21] Stepankova H.: Anizotropie hyperjemneho pole ve ferimagnetickych oxidech,habilitacnı prace, MFF UK, Praha, 1999.

[22] Chlan V., Novak P., Stepankova H., Reznıcek R., Kouril K., Koz lowski A.(2009): Electronic structure and hyperfine fields in non-stoichiometric mag-netite above the Verwey transition, J. Magn. Magn. Mater., article in press,doi:10.1016/j.jmmm.2009.03.026

[23] Novak P., Stepankova H., Englich J., Kohout J., Brabers V. A. M. (2000):Temperature Dependence of NMR in Magnetite, Ferrites, Proceedings of theEight International Conference on Ferrites, 2000, Kyoto, p. 131–134.

[24] Kakol Z., Sabol J., Stickler J., Honig J. M. (1992): Effect of low-level tita-nium(IV) doping on the resistivity of magnetite near the Verwey transition,Phys. Rev. B 46, 1975–1978.

[25] Honig J. M. (1995): Analysis of the Verwey transition in magnetite, J. AlloysCompd. 229, 24–39.

[26] Gamaliy O.: Hyperfine interactions in magnetic iron oxides with nonmagneticsubstitutions, Doctoral Thesis, MFF UK, Prague, 2006.

112

[27] Kokalj. A. (2003): Computer graphics and graphical user interfaces as toolsin simulations of matter at the atomic scale, Comp. Mater. Sci. 28, 155–168.Code available from http://www.xcrysden.org/.

[28] Ba landa M., Wiechec A., Kim D., Kakol Z., Koz lowski A., Niedziela P.,Sabol J., Tarnawski Z., Honig J. M. (2005): Magnetic AC susceptibility ofstoichiometric and low zin doped magnetite single crystals, Eur. Phys. J. B43, 201–212.

[29] Brabers V. A. M., Whall T. E., Knapen P. S. A. (1984): Preparation ofpolycrystalline and monocrystalline Fe3−xTixO4 spinels, J. Cryst. Growth 69,101-107.

[30] Kohout J., Kouril K., Chlan V., Stepankova H.: Unpublished results on agallium substituted magnetite

[31] Kovtun N. M., Koteleva A. M., Moskvin A. S., Shemyakov A. A. (1989):Navedennye sverchtonkie vzaimodejstvija na jadrach ionov O2− v ferritach-spinelach, Zhurnal eksperimentalnoi i teoreticheskoi fiziki 95, 1459–1466

[32] Novak P., Englich J., Stepankova H., Kohout J., Lutgemeier H., Wagner K.,Tolksdorf W. (1997): Antisite defects in yttrium iron garnet, J. Phys. IVFrance 7, C1-283 – C1-287

113

Influence of cationic substitution on hyperfine...

Documents

Transcript of Influence of cationic substitution on hyperfine...